LMFDB - Embedded newform 225.2.q.a.121.22

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [225,2,Mod(16,225)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(225, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([20, 6]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("225.16");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 225 = 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	225.q (of order $15$, degree $8$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$1.79663404548$
Analytic rank:	$0$
Dimension:	$224$
Relative dimension:	$28$ over $\Q(\zeta_{15})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			121.22
Character	$\chi$	$=$	225.121
Dual form			225.2.q.a.106.22

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.62705 - 0.345839i) q^{2} +(1.73185 + 0.0263451i) q^{3} +(0.700584 - 0.311920i) q^{4} +(-0.380412 - 2.20347i) q^{5} +(2.82691 - 0.556077i) q^{6} +(0.694163 + 1.20233i) q^{7} +(-1.65942 + 1.20564i) q^{8} +(2.99861 + 0.0912516i) q^{9} +(-1.38100 - 3.45359i) q^{10} +(-4.44787 + 0.945423i) q^{11} +(1.22152 - 0.521742i) q^{12} +(-0.664131 - 0.141165i) q^{13} +(1.54525 + 1.71617i) q^{14} +(-0.600766 - 3.82611i) q^{15} +(-3.30929 + 3.67534i) q^{16} +(-1.73545 + 1.26088i) q^{17} +(4.91044 - 0.888568i) q^{18} +(5.56870 - 4.04590i) q^{19} +(-0.953818 - 1.42506i) q^{20} +(1.17051 + 2.10054i) q^{21} +(-6.90992 + 3.07649i) q^{22} +(-0.0716950 - 0.0796254i) q^{23} +(-2.90563 + 2.04427i) q^{24} +(-4.71057 + 1.67645i) q^{25} -1.12939 q^{26} +(5.19074 + 0.237033i) q^{27} +(0.861350 + 0.625807i) q^{28} +(-0.214650 + 2.04226i) q^{29} +(-2.30069 - 6.01748i) q^{30} +(0.675922 + 6.43096i) q^{31} +(-2.06213 + 3.57172i) q^{32} +(-7.72795 + 1.52015i) q^{33} +(-2.38760 + 2.65170i) q^{34} +(2.38522 - 1.98695i) q^{35} +(2.12924 - 0.871398i) q^{36} +(-0.886060 - 2.72701i) q^{37} +(7.66130 - 8.50874i) q^{38} +(-1.14646 - 0.261974i) q^{39} +(3.28786 + 3.19785i) q^{40} +(-5.31403 - 1.12953i) q^{41} +(2.63092 + 3.01286i) q^{42} +(-0.613014 - 1.06177i) q^{43} +(-2.82121 + 2.04973i) q^{44} +(-0.939638 - 6.64207i) q^{45} +(-0.144189 - 0.104759i) q^{46} +(1.23665 - 11.7660i) q^{47} +(-5.82802 + 6.27796i) q^{48} +(2.53627 - 4.39296i) q^{49} +(-7.08454 + 4.35677i) q^{50} +(-3.03876 + 2.13793i) q^{51} +(-0.509312 + 0.108258i) q^{52} +(-1.07586 - 0.781661i) q^{53} +(8.52756 - 1.40950i) q^{54} +(3.77524 + 9.44110i) q^{55} +(-2.60148 - 1.15825i) q^{56} +(9.75074 - 6.86018i) q^{57} +(0.357048 + 3.39709i) q^{58} +(1.69407 + 0.360086i) q^{59} +(-1.61433 - 2.49312i) q^{60} +(3.69259 - 0.784884i) q^{61} +(3.32384 + 10.2297i) q^{62} +(1.97181 + 3.66865i) q^{63} +(0.936638 - 2.88268i) q^{64} +(-0.0584104 + 1.51709i) q^{65} +(-12.0480 + 5.14599i) q^{66} +(1.48608 + 14.1391i) q^{67} +(-0.822536 + 1.42467i) q^{68} +(-0.122067 - 0.139788i) q^{69} +(3.19370 - 4.05776i) q^{70} +(-10.9600 - 7.96294i) q^{71} +(-5.08598 + 3.46382i) q^{72} +(-1.83085 + 5.63478i) q^{73} +(-2.38477 - 4.13054i) q^{74} +(-8.20217 + 2.77927i) q^{75} +(2.63935 - 4.57148i) q^{76} +(-4.22425 - 4.69151i) q^{77} +(-1.95594 - 0.0297540i) q^{78} +(0.938478 - 8.92902i) q^{79} +(9.35740 + 5.89378i) q^{80} +(8.98335 + 0.547256i) q^{81} -9.03682 q^{82} +(16.5673 + 7.37623i) q^{83} +(1.47524 + 1.10650i) q^{84} +(3.43850 + 3.34436i) q^{85} +(-1.36460 - 1.51555i) q^{86} +(-0.425545 + 3.53123i) q^{87} +(6.24105 - 6.93138i) q^{88} +(2.33361 - 7.18212i) q^{89} +(-3.82592 - 10.4820i) q^{90} +(-0.291288 - 0.896494i) q^{91} +(-0.0750652 - 0.0334212i) q^{92} +(1.00117 + 11.1553i) q^{93} +(-2.05704 - 19.5715i) q^{94} +(-11.0334 - 10.7314i) q^{95} +(-3.66541 + 6.13136i) q^{96} +(-1.13640 + 10.8121i) q^{97} +(2.60738 - 8.02469i) q^{98} +(-13.4237 + 2.42908i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 224 q - 3 q^{2} - 8 q^{3} + 23 q^{4} - 8 q^{5} - 10 q^{6} - 8 q^{7} - 20 q^{8} - 8 q^{9} - 20 q^{10} - 11 q^{11} - 4 q^{12} - 3 q^{13} + q^{14} - 48 q^{15} + 23 q^{16} - 24 q^{17} - 12 q^{19} + q^{20}+ \cdots - 20 q^{99}+O(q^{100}) $ 224 * q - 3 * q^2 - 8 * q^3 + 23 * q^4 - 8 * q^5 - 10 * q^6 - 8 * q^7 - 20 * q^8 - 8 * q^9 - 20 * q^10 - 11 * q^11 - 4 * q^12 - 3 * q^13 + q^14 - 48 * q^15 + 23 * q^16 - 24 * q^17 - 12 * q^19 + q^20 + 15 * q^21 - 11 * q^22 + q^23 - 30 * q^24 - 16 * q^25 - 136 * q^26 + 7 * q^27 + 4 * q^28 - 15 * q^29 - 24 * q^30 + 3 * q^31 + 12 * q^32 - 5 * q^33 + q^34 + 14 * q^35 + 38 * q^36 - 24 * q^37 + 55 * q^38 + 20 * q^39 + q^40 - 19 * q^41 - 38 * q^42 - 8 * q^43 + 4 * q^44 - 38 * q^45 - 20 * q^46 - 10 * q^47 - 25 * q^48 - 72 * q^49 - 3 * q^50 - 26 * q^51 - 25 * q^52 - 12 * q^53 + 53 * q^54 - 20 * q^55 - 60 * q^56 + 38 * q^57 - 23 * q^58 - 30 * q^59 - 33 * q^60 - 3 * q^61 - 44 * q^62 + 46 * q^63 - 44 * q^64 + 51 * q^65 - 134 * q^66 - 12 * q^67 - 156 * q^68 + 4 * q^69 - 16 * q^70 + 42 * q^71 + 74 * q^72 - 12 * q^73 + 90 * q^74 + 67 * q^75 - 8 * q^76 + 31 * q^77 - 92 * q^78 - 15 * q^79 + 298 * q^80 - 104 * q^81 + 8 * q^82 + 59 * q^83 + 115 * q^84 - 11 * q^85 + 9 * q^86 - 59 * q^87 - 23 * q^88 + 106 * q^89 + 107 * q^90 + 30 * q^91 + 11 * q^92 + 32 * q^93 + 25 * q^94 + 7 * q^95 + 35 * q^96 - 21 * q^97 + 146 * q^98 - 20 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/225\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{3}{5}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	1.62705	−	0.345839i	1.15050	−	0.244545i	0.407091	−	0.913388i	$-0.366543\pi$
$2$	1.62705	−	0.345839i	1.15050	−	0.244545i	0.743404	+	0.668842i	$0.233210\pi$
$3$	1.73185	+	0.0263451i	0.999884	+	0.0152104i
$3$	1.73185	+	0.0263451i	0.999884	+	0.0152104i
$4$	0.700584	−	0.311920i	0.350292	−	0.155960i
$5$	−0.380412	−	2.20347i	−0.170126	−	0.985422i
$5$	−0.380412	−	2.20347i	−0.170126	−	0.985422i
$6$	2.82691	−	0.556077i	1.15408	−	0.227018i
$7$	0.694163	+	1.20233i	0.262369	+	0.454436i	0.966871	−	0.255266i	$-0.0821629\pi$
$7$	0.694163	+	1.20233i	0.262369	+	0.454436i	−0.704502	+	0.709702i	$0.748830\pi$
$8$	−1.65942	+	1.20564i	−0.586694	+	0.426258i
$9$	2.99861	+	0.0912516i	0.999537	+	0.0304172i
$10$	−1.38100	−	3.45359i	−0.436709	−	1.09212i
$11$	−4.44787	+	0.945423i	−1.34108	+	0.285056i	−0.821912	−	0.569615i	$-0.807092\pi$
$11$	−4.44787	+	0.945423i	−1.34108	+	0.285056i	−0.519170	+	0.854671i	$0.673759\pi$
$12$	1.22152	−	0.521742i	0.352624	−	0.150614i
$13$	−0.664131	−	0.141165i	−0.184197	−	0.0391522i	0.114890	−	0.993378i	$-0.463349\pi$
$13$	−0.664131	−	0.141165i	−0.184197	−	0.0391522i	−0.299086	+	0.954226i	$0.596682\pi$
$14$	1.54525	+	1.71617i	0.412985	+	0.458666i
$15$	−0.600766	−	3.82611i	−0.155117	−	0.987896i
$16$	−3.30929	+	3.67534i	−0.827323	+	0.918835i
$17$	−1.73545	+	1.26088i	−0.420909	+	0.305808i	−0.778003	−	0.628260i	$-0.783767\pi$
$17$	−1.73545	+	1.26088i	−0.420909	+	0.305808i	0.357095	+	0.934068i	$0.383767\pi$
$18$	4.91044	−	0.888568i	1.15740	−	0.209437i
$19$	5.56870	−	4.04590i	1.27755	−	0.928192i	0.278071	−	0.960560i	$-0.410305\pi$
$19$	5.56870	−	4.04590i	1.27755	−	0.928192i	0.999476	+	0.0323680i	$0.0103049\pi$
$20$	−0.953818	−	1.42506i	−0.213280	−	0.318653i
$21$	1.17051	+	2.10054i	0.255427	+	0.458375i
$22$	−6.90992	+	3.07649i	−1.47320	+	0.655911i
$23$	−0.0716950	−	0.0796254i	−0.0149494	−	0.0166030i	0.735624	−	0.677390i	$-0.236889\pi$
$23$	−0.0716950	−	0.0796254i	−0.0149494	−	0.0166030i	−0.750573	+	0.660787i	$0.770223\pi$
$24$	−2.90563	+	2.04427i	−0.593110	+	0.417285i
$25$	−4.71057	+	1.67645i	−0.942115	+	0.335291i
$26$	−1.12939			−0.221492
$27$	5.19074	+	0.237033i	0.998959	+	0.0456170i
$28$	0.861350	+	0.625807i	0.162780	+	0.118266i
$29$	−0.214650	+	2.04226i	−0.0398595	+	0.379238i	0.956348	+	0.292230i	$0.0943973\pi$
$29$	−0.214650	+	2.04226i	−0.0398595	+	0.379238i	−0.996208	+	0.0870081i	$0.972269\pi$
$30$	−2.30069	−	6.01748i	−0.420047	−	1.09864i
$31$	0.675922	+	6.43096i	0.121399	+	1.15504i	0.870358	+	0.492419i	$0.163887\pi$
$31$	0.675922	+	6.43096i	0.121399	+	1.15504i	−0.748959	+	0.662616i	$0.769446\pi$
$32$	−2.06213	+	3.57172i	−0.364537	+	0.631397i
$33$	−7.72795	+	1.52015i	−1.34526	+	0.264625i
$34$	−2.38760	+	2.65170i	−0.409470	+	0.454762i
$35$	2.38522	−	1.98695i	0.403176	−	0.335856i
$36$	2.12924	−	0.871398i	0.354874	−	0.145233i
$37$	−0.886060	−	2.72701i	−0.145667	−	0.448318i	0.851429	−	0.524470i	$-0.175737\pi$
$37$	−0.886060	−	2.72701i	−0.145667	−	0.448318i	−0.997096	+	0.0761520i	$0.975737\pi$
$38$	7.66130	−	8.50874i	1.24283	−	1.38030i
$39$	−1.14646	−	0.261974i	−0.183580	−	0.0419494i
$40$	3.28786	+	3.19785i	0.519856	+	0.505624i
$41$	−5.31403	−	1.12953i	−0.829913	−	0.176403i	−0.226681	−	0.973969i	$-0.572787\pi$
$41$	−5.31403	−	1.12953i	−0.829913	−	0.176403i	−0.603232	+	0.797566i	$0.706121\pi$
$42$	2.63092	+	3.01286i	0.405960	+	0.464895i
$43$	−0.613014	−	1.06177i	−0.0934837	−	0.161919i	0.815491	−	0.578770i	$-0.196467\pi$
$43$	−0.613014	−	1.06177i	−0.0934837	−	0.161919i	−0.908975	+	0.416851i	$0.863134\pi$
$44$	−2.82121	+	2.04973i	−0.425313	+	0.309008i
$45$	−0.939638	−	6.64207i	−0.140073	−	0.990141i
$46$	−0.144189	−	0.104759i	−0.0212595	−	0.0154459i
$47$	1.23665	−	11.7660i	0.180385	−	1.71624i	−0.412501	−	0.910957i	$-0.635345\pi$
$47$	1.23665	−	11.7660i	0.180385	−	1.71624i	0.592885	−	0.805287i	$-0.297989\pi$
$48$	−5.82802	+	6.27796i	−0.841203	+	0.906145i
$49$	2.53627	−	4.39296i	0.362325	−	0.627565i
$50$	−7.08454	+	4.35677i	−1.00190	+	0.616141i
$51$	−3.03876	+	2.13793i	−0.425512	+	0.299371i
$52$	−0.509312	+	0.108258i	−0.0706289	+	0.0150126i
$53$	−1.07586	−	0.781661i	−0.147781	−	0.107369i	0.511438	−	0.859320i	$-0.329113\pi$
$53$	−1.07586	−	0.781661i	−0.147781	−	0.107369i	−0.659219	+	0.751951i	$0.729113\pi$
$54$	8.52756	−	1.40950i	1.16045	−	0.191809i
$55$	3.77524	+	9.44110i	0.509053	+	1.27304i
$56$	−2.60148	−	1.15825i	−0.347638	−	0.154778i
$57$	9.75074	−	6.86018i	1.29152	−	0.908653i
$58$	0.357048	+	3.39709i	0.0468827	+	0.446059i
$59$	1.69407	+	0.360086i	0.220549	+	0.0468792i	0.316861	−	0.948472i	$-0.397371\pi$
$59$	1.69407	+	0.360086i	0.220549	+	0.0468792i	−0.0963115	+	0.995351i	$0.530705\pi$
$60$	−1.61433	−	2.49312i	−0.208409	−	0.321860i
$61$	3.69259	−	0.784884i	0.472788	−	0.100494i	0.0346452	−	0.999400i	$-0.488970\pi$
$61$	3.69259	−	0.784884i	0.472788	−	0.100494i	0.438142	+	0.898906i	$0.355637\pi$
$62$	3.32384	+	10.2297i	0.422128	+	1.29918i
$63$	1.97181	+	3.66865i	0.248425	+	0.462207i
$64$	0.936638	−	2.88268i	0.117080	−	0.360334i
$65$	−0.0584104	+	1.51709i	−0.00724492	+	0.188172i
$66$	−12.0480	+	5.14599i	−1.48301	+	0.633427i
$67$	1.48608	+	14.1391i	0.181553	+	1.72737i	0.583854	+	0.811858i	$0.301544\pi$
$67$	1.48608	+	14.1391i	0.181553	+	1.72737i	−0.402301	+	0.915508i	$0.631789\pi$
$68$	−0.822536	+	1.42467i	−0.0997472	+	0.172767i
$69$	−0.122067	−	0.139788i	−0.0146952	−	0.0168285i
$70$	3.19370	−	4.05776i	0.381721	−	0.484995i
$71$	−10.9600	−	7.96294i	−1.30072	−	0.945027i	−0.300755	−	0.953701i	$-0.597239\pi$
$71$	−10.9600	−	7.96294i	−1.30072	−	0.945027i	−0.999962	+	0.00867479i	$0.997239\pi$
$72$	−5.08598	+	3.46382i	−0.599388	+	0.408215i
$73$	−1.83085	+	5.63478i	−0.214285	+	0.659501i	0.784919	+	0.619599i	$0.212705\pi$
$73$	−1.83085	+	5.63478i	−0.214285	+	0.659501i	−0.999204	+	0.0399023i	$0.987295\pi$
$74$	−2.38477	−	4.13054i	−0.277224	−	0.480166i
$75$	−8.20217	+	2.77927i	−0.947106	+	0.320922i
$76$	2.63935	−	4.57148i	0.302754	−	0.524385i
$77$	−4.22425	−	4.69151i	−0.481398	−	0.534647i
$78$	−1.95594	−	0.0297540i	−0.221466	−	0.00336897i
$79$	0.938478	−	8.92902i	0.105587	−	1.00459i	−0.805561	−	0.592513i	$-0.798136\pi$
$79$	0.938478	−	8.92902i	0.105587	−	1.00459i	0.911148	−	0.412080i	$-0.135198\pi$
$80$	9.35740	+	5.89378i	1.04619	+	0.658945i
$81$	8.98335	+	0.547256i	0.998150	+	0.0608062i
$82$	−9.03682			−0.997950
$83$	16.5673	+	7.37623i	1.81850	+	0.809647i	0.948653	+	0.316320i	$0.102447\pi$
$83$	16.5673	+	7.37623i	1.81850	+	0.809647i	0.869844	+	0.493327i	$0.164219\pi$
$84$	1.47524	+	1.10650i	0.160962	+	0.120729i
$85$	3.43850	+	3.34436i	0.372958	+	0.362747i
$86$	−1.36460	−	1.51555i	−0.147149	−	0.163426i
$87$	−0.425545	+	3.53123i	−0.0456233	+	0.378588i
$88$	6.24105	−	6.93138i	0.665298	−	0.738888i
$89$	2.33361	−	7.18212i	0.247363	−	0.761304i	−0.747876	−	0.663838i	$-0.768926\pi$
$89$	2.33361	−	7.18212i	0.247363	−	0.761304i	0.995239	−	0.0974656i	$-0.0310736\pi$
$90$	−3.82592	−	10.4820i	−0.403288	−	1.10490i
$91$	−0.291288	−	0.896494i	−0.0305353	−	0.0939781i
$92$	−0.0750652	−	0.0334212i	−0.00782608	−	0.00348440i
$93$	1.00117	+	11.1553i	0.103817	+	1.15675i
$94$	−2.05704	−	19.5715i	−0.212168	−	2.01864i
$95$	−11.0334	−	10.7314i	−1.13200	−	1.10101i
$96$	−3.66541	+	6.13136i	−0.374099	+	0.625779i
$97$	−1.13640	+	10.8121i	−0.115384	+	1.09781i	0.771633	+	0.636068i	$0.219440\pi$
$97$	−1.13640	+	10.8121i	−0.115384	+	1.09781i	−0.887017	+	0.461737i	$0.847226\pi$
$98$	2.60738	−	8.02469i	0.263385	−	0.810616i
$99$	−13.4237	+	2.42908i	−1.34913	+	0.244132i
$100$	−2.77723	+	2.64382i	−0.277723	+	0.264382i
$101$	−6.10657	−	10.5769i	−0.607626	−	1.05244i	−0.991630	−	0.129108i	$-0.958788\pi$
$101$	−6.10657	−	10.5769i	−0.607626	−	1.05244i	0.384004	−	0.923331i	$-0.374545\pi$
$102$	−4.20482	+	4.52944i	−0.416340	+	0.448481i
$103$	−0.775688	+	0.345359i	−0.0764309	+	0.0340292i	−0.444596	−	0.895731i	$-0.646653\pi$
$103$	−0.775688	+	0.345359i	−0.0764309	+	0.0340292i	0.368165	+	0.929760i	$0.379986\pi$
$104$	1.27227	−	0.566450i	0.124756	−	0.0555450i
$105$	4.18320	−	3.37826i	0.408238	−	0.329684i
$106$	−2.02081	−	0.899723i	−0.196278	−	0.0873888i
$107$	19.0764			1.84419			0.922095	−	0.386964i	$-0.126476\pi$
$107$	19.0764			1.84419			0.922095	+	0.386964i	$0.126476\pi$
$108$	3.71049	−	1.45304i	0.357042	−	0.139818i
$109$	4.05014	+	12.4651i	0.387933	+	1.19394i	0.934330	+	0.356409i	$0.115999\pi$
$109$	4.05014	+	12.4651i	0.387933	+	1.19394i	−0.546397	+	0.837526i	$0.684001\pi$
$110$	9.40759	+	14.0555i	0.896978	+	1.34014i
$111$	−1.46268	−	4.74612i	−0.138831	−	0.450482i
$112$	−6.71614	−	1.42756i	−0.634616	−	0.134892i
$113$	6.81089	+	1.44770i	0.640714	+	0.136188i	0.516802	−	0.856105i	$-0.327122\pi$
$113$	6.81089	+	1.44770i	0.640714	+	0.136188i	0.123913	+	0.992293i	$0.460456\pi$
$114$	13.4924	−	14.5340i	1.26368	−	1.36124i
$115$	−0.148179	+	0.188268i	−0.0138177	+	0.0175561i
$116$	0.486642	+	1.49773i	0.0451835	+	0.139061i
$117$	−1.97859	−	0.483903i	−0.182921	−	0.0447369i
$118$	2.88087			0.265205
$119$	−2.72067	−	1.21132i	−0.249404	−	0.111042i
$120$	5.60983	+	5.62481i	0.512105	+	0.513473i
$121$	8.84069	−	3.93613i	0.803699	−	0.357830i
$122$	5.73657	−	2.55409i	0.519365	−	0.231236i
$123$	−9.17336	−	2.09618i	−0.827134	−	0.189006i
$124$	2.47949	+	4.29460i	0.222665	+	0.385666i
$125$	5.48598	+	9.74187i	0.490681	+	0.871339i
$126$	4.47699	+	5.28714i	0.398842	+	0.471016i
$127$	6.85641	−	21.1019i	0.608408	−	1.87249i	0.137000	−	0.990571i	$-0.456254\pi$
$127$	6.85641	−	21.1019i	0.608408	−	1.87249i	0.471407	−	0.881916i	$-0.343746\pi$
$128$	1.38922	−	13.2175i	0.122791	−	1.16828i
$129$	−1.03368	−	1.85498i	−0.0910101	−	0.163322i
$130$	0.429635	+	2.48858i	0.0376814	+	0.218263i
$131$	1.21480	+	11.5581i	0.106138	+	1.00983i	0.909885	+	0.414862i	$0.136170\pi$
$131$	1.21480	+	11.5581i	0.106138	+	1.00983i	−0.803747	+	0.594972i	$0.797163\pi$
$132$	−4.93991	+	3.47550i	−0.429964	+	0.302503i
$133$	8.73007	+	3.88688i	0.756993	+	0.337035i
$134$	7.30778	+	22.4910i	0.631296	+	1.94293i
$135$	−1.45233	−	11.5278i	−0.124996	−	0.992157i
$136$	1.35968	−	4.18466i	0.116591	−	0.358832i
$137$	−11.0828	+	12.3087i	−0.946869	+	1.05160i	0.0517289	+	0.998661i	$0.483527\pi$
$137$	−11.0828	+	12.3087i	−0.946869	+	1.05160i	−0.998598	+	0.0529430i	$0.983140\pi$
$138$	−0.246953	−	0.185226i	−0.0210221	−	0.0157675i
$139$	−11.2616	−	12.5073i	−0.955198	−	1.06085i	−0.998090	−	0.0617748i	$-0.980324\pi$
$139$	−11.2616	−	12.5073i	−0.955198	−	1.06085i	0.0428925	−	0.999080i	$-0.486343\pi$
$140$	1.05128	−	2.13602i	0.0888494	−	0.180527i
$141$	2.45168	−	20.3443i	0.206468	−	1.71330i
$142$	−20.5864	−	9.16565i	−1.72757	−	0.769164i
$143$	3.08743			0.258184
$144$	−10.2587	+	10.7189i	−0.854888	+	0.893245i
$145$	4.58172	−	0.303925i	0.380491	−	0.0252396i
$146$	−1.03015	+	9.80123i	−0.0852559	+	0.811155i
$147$	4.50818	−	7.54113i	0.371829	−	0.621982i
$148$	−1.47137	−	1.63412i	−0.120946	−	0.134324i
$149$	−7.97992	+	13.8216i	−0.653740	+	1.13231i	0.328468	+	0.944515i	$0.393468\pi$
$149$	−7.97992	+	13.8216i	−0.653740	+	1.13231i	−0.982208	+	0.187796i	$0.939865\pi$
$150$	−12.3841	+	7.35863i	−1.01116	+	0.600830i
$151$	−4.20769	−	7.28793i	−0.342417	−	0.593084i	0.642464	−	0.766316i	$-0.277912\pi$
$151$	−4.20769	−	7.28793i	−0.342417	−	0.593084i	−0.984881	+	0.173232i	$0.944579\pi$
$152$	−4.36292	+	13.4277i	−0.353880	+	1.08913i
$153$	−5.31900	+	3.62253i	−0.430016	+	0.292864i
$154$	−8.49556	−	6.17239i	−0.684592	−	0.497385i
$155$	13.9133	−	3.93579i	1.11754	−	0.316130i
$156$	−0.884904	+	0.174068i	−0.0708490	+	0.0139366i
$157$	0.0425739	−	0.0737402i	0.00339777	−	0.00588511i	−0.864322	−	0.502940i	$-0.832252\pi$
$157$	0.0425739	−	0.0737402i	0.00339777	−	0.00588511i	0.867719	+	0.497055i	$0.165585\pi$
$158$	−1.56106	−	14.8525i	−0.124191	−	1.18160i
$159$	−1.84264	−	1.38206i	−0.146131	−	0.109605i
$160$	8.65465	+	3.18513i	0.684210	+	0.251806i
$161$	0.0459676	−	0.141474i	0.00362275	−	0.0111497i
$162$	14.8056	−	2.21638i	1.16324	−	0.174136i
$163$	3.81218	+	11.7327i	0.298593	+	0.918974i	0.981991	+	0.188928i	$0.0605013\pi$
$163$	3.81218	+	11.7327i	0.298593	+	0.918974i	−0.683398	+	0.730046i	$0.739499\pi$
$164$	−4.07525	+	0.866222i	−0.318224	+	0.0676406i
$165$	6.28942	+	16.4500i	0.489630	+	1.28063i
$166$	29.5067	+	6.27185i	2.29017	+	0.486790i
$167$	0.700044	+	6.66047i	0.0541710	+	0.515403i	0.987639	+	0.156743i	$0.0500994\pi$
$167$	0.700044	+	6.66047i	0.0541710	+	0.515403i	−0.933468	+	0.358660i	$0.883234\pi$
$168$	−4.47486	−	2.07446i	−0.345243	−	0.160048i
$169$	−11.4549	−	5.10007i	−0.881150	−	0.392313i
$170$	6.75121	+	4.25227i	0.517794	+	0.326134i
$171$	17.0676	−	11.6239i	1.30519	−	0.888904i
$172$	−0.760656	−	0.552649i	−0.0579995	−	0.0421391i
$173$	−11.2482	+	2.39087i	−0.855181	+	0.181774i	−0.614585	−	0.788851i	$-0.710676\pi$
$173$	−11.2482	+	2.39087i	−0.855181	+	0.181774i	−0.240596	+	0.970625i	$0.577343\pi$
$174$	0.528857	+	5.89265i	0.0400926	+	0.446721i
$175$	−5.28555	−	4.49991i	−0.399550	−	0.340161i
$176$	11.2445	−	19.4761i	0.847588	−	1.46807i
$177$	2.92439	+	0.668246i	0.219811	+	0.0502284i
$178$	1.31304	−	12.4927i	0.0984162	−	0.936368i
$179$	−3.97320	−	2.88670i	−0.296971	−	0.215762i	0.429315	−	0.903155i	$-0.358755\pi$
$179$	−3.97320	−	2.88670i	−0.296971	−	0.215762i	−0.726286	+	0.687393i	$0.758755\pi$
$180$	−2.73009	−	4.36024i	−0.203489	−	0.324993i
$181$	−1.69167	+	1.22907i	−0.125741	+	0.0913562i	−0.648878	−	0.760892i	$-0.724762\pi$
$181$	−1.69167	+	1.22907i	−0.125741	+	0.0913562i	0.523137	+	0.852248i	$0.324762\pi$
$182$	−0.783983	−	1.35790i	−0.0581127	−	0.100654i
$183$	6.41569	−	1.26202i	0.474261	−	0.0932912i
$184$	0.214972	+	0.0456937i	0.0158479	+	0.00336858i
$185$	−5.67183	+	2.98980i	−0.417001	+	0.219814i
$186$	5.48688	+	17.8039i	0.402318	+	1.30545i
$187$	6.52699	−	7.24896i	0.477301	−	0.530096i
$188$	−2.80367	−	8.62880i	−0.204478	−	0.629320i
$189$	3.31823	+	6.40550i	0.241366	+	0.465932i
$190$	−21.6632	−	13.6446i	−1.57161	−	0.989886i
$191$	6.87172	−	7.63182i	0.497220	−	0.552219i	−0.441337	−	0.897341i	$-0.645496\pi$
$191$	6.87172	−	7.63182i	0.497220	−	0.552219i	0.938558	+	0.345122i	$0.112162\pi$
$192$	1.69806	−	4.96769i	0.122547	−	0.358512i
$193$	0.879316	−	1.52302i	0.0632945	−	0.109629i	−0.832642	−	0.553812i	$-0.813173\pi$
$193$	0.879316	−	1.52302i	0.0632945	−	0.109629i	0.895936	+	0.444183i	$0.146506\pi$
$194$	1.89028	+	17.9848i	0.135714	+	1.29124i
$195$	−0.141126	+	2.62584i	−0.0101062	+	0.188040i
$196$	0.406622	−	3.86875i	0.0290444	−	0.276339i
$197$	1.28192	+	0.931373i	0.0913333	+	0.0663576i	0.632515	−	0.774548i	$-0.282023\pi$
$197$	1.28192	+	0.931373i	0.0913333	+	0.0663576i	−0.541181	+	0.840906i	$0.682023\pi$
$198$	−21.0009	+	8.59467i	−1.49247	+	0.610797i
$199$	−4.83781			−0.342943			−0.171471	−	0.985189i	$-0.554852\pi$
$199$	−4.83781			−0.342943			−0.171471	+	0.985189i	$0.554852\pi$
$200$	5.79563	−	8.46120i	0.409813	−	0.598297i
$201$	2.20117	+	24.5260i	0.155259	+	1.72993i
$202$	−13.5936	−	15.0972i	−0.956441	−	1.06224i
$203$	−2.60446	+	1.15958i	−0.182798	+	0.0813867i
$204$	−1.46204	+	2.44565i	−0.102364	+	0.171230i
$205$	−0.467370	+	12.1390i	−0.0326425	+	0.847825i
$206$	−1.14264	+	0.830178i	−0.0796117	+	0.0578413i
$207$	−0.207720	−	0.245308i	−0.0144375	−	0.0170501i
$208$	2.71663	−	1.97375i	0.188365	−	0.136855i
$209$	−20.9437	+	23.2604i	−1.44871	+	1.60895i
$210$	5.63792	−	6.94330i	0.389053	−	0.479133i
$211$	−2.87300	−	3.19079i	−0.197785	−	0.219663i	0.636091	−	0.771614i	$-0.280550\pi$
$211$	−2.87300	−	3.19079i	−0.197785	−	0.219663i	−0.833877	+	0.551951i	$0.813884\pi$
$212$	−0.997550	−	0.212036i	−0.0685120	−	0.0145627i
$213$	−18.7714	−	14.0794i	−1.28619	−	0.964702i
$214$	31.0383	−	6.59739i	2.12173	−	0.450988i
$215$	−2.10638	+	1.75467i	−0.143654	+	0.119667i
$216$	−8.89941	+	5.86483i	−0.605528	+	0.399051i
$217$	−7.26291	+	5.27682i	−0.493039	+	0.358214i
$218$	10.9007	+	18.8805i	0.738287	+	1.27875i
$219$	−3.31921	+	9.71036i	−0.224291	+	0.656165i
$220$	5.58974	+	5.43671i	0.376860	+	0.366543i
$221$	1.33056	−	0.592403i	0.0895031	−	0.0398494i
$222$	−4.02125	−	7.21631i	−0.269888	−	0.484327i
$223$	−15.8538	+	3.36984i	−1.06165	+	0.225661i	−0.705459	−	0.708751i	$-0.749259\pi$
$223$	−15.8538	+	3.36984i	−1.06165	+	0.225661i	−0.356193	+	0.934412i	$0.615926\pi$
$224$	−5.72583			−0.382573
$225$	−14.2782	+	4.59719i	−0.951877	+	0.306479i
$226$	11.5823			0.770443
$227$	−9.01077	+	1.91530i	−0.598066	+	0.127123i	−0.496990	−	0.867756i	$-0.665562\pi$
$227$	−9.01077	+	1.91530i	−0.598066	+	0.127123i	−0.101075	+	0.994879i	$0.532228\pi$
$228$	4.69139	−	7.84759i	0.310695	−	0.519719i
$229$	−7.49545	+	3.33719i	−0.495314	+	0.220528i	−0.639162	−	0.769072i	$-0.720719\pi$
$229$	−7.49545	+	3.33719i	−0.495314	+	0.220528i	0.143849	+	0.989600i	$0.454052\pi$
$230$	−0.175983	+	0.357567i	−0.0116040	+	0.0235773i
$231$	−7.19217	−	8.23628i	−0.473210	−	0.541907i
$232$	−2.10604	−	3.64776i	−0.138268	−	0.239487i
$233$	−6.70215	+	4.86940i	−0.439073	+	0.319005i	−0.785266	−	0.619158i	$-0.787474\pi$
$233$	−6.70215	+	4.86940i	−0.439073	+	0.319005i	0.346194	+	0.938163i	$0.387474\pi$
$234$	−3.38661	−	0.103059i	−0.221390	−	0.00673717i
$235$	−26.3964	+	1.75099i	−1.72191	+	0.114222i
$236$	1.29916	−	0.276145i	0.0845680	−	0.0179755i
$237$	1.86054	−	15.4390i	0.120855	−	1.00287i
$238$	−4.84559	−	1.02996i	−0.314093	−	0.0667625i
$239$	0.722110	+	0.801984i	0.0467094	+	0.0518760i	0.766047	−	0.642785i	$-0.222221\pi$
$239$	0.722110	+	0.801984i	0.0467094	+	0.0518760i	−0.719337	+	0.694661i	$0.755554\pi$
$240$	16.0503	+	10.4537i	1.03605	+	0.674782i
$241$	−16.7927	+	18.6502i	−1.08172	+	1.20137i	−0.103315	+	0.994649i	$0.532945\pi$
$241$	−16.7927	+	18.6502i	−1.08172	+	1.20137i	−0.978401	+	0.206718i	$0.933722\pi$
$242$	13.0229	−	9.46173i	0.837147	−	0.608223i
$243$	15.5434	+	1.18443i	0.997109	+	0.0759814i
$244$	2.34215	−	1.70167i	0.149941	−	0.108938i
$245$	−10.6446	−	3.91748i	−0.680058	−	0.250278i
$246$	−15.6504	−	0.238076i	−0.997834	−	0.0151792i
$247$	−4.26949	+	1.90090i	−0.271661	+	0.120951i
$248$	−8.87507	−	9.85676i	−0.563567	−	0.625905i
$249$	28.4977	+	13.2110i	1.80597	+	0.837213i
$250$	12.2951	+	13.9532i	0.777608	+	0.882478i
$251$	−23.1900			−1.46374			−0.731869	−	0.681445i	$-0.761352\pi$
$251$	−23.1900			−1.46374			−0.731869	+	0.681445i	$0.761352\pi$
$252$	2.52575	+	1.95515i	0.159107	+	0.123163i
$253$	0.394169	+	0.286381i	0.0247812	+	0.0180046i
$254$	3.85784	−	36.7049i	0.242062	−	2.30307i
$255$	5.86686	+	5.88253i	0.367397	+	0.368378i
$256$	−1.67716	−	15.9571i	−0.104823	−	0.997321i
$257$	−10.4244	+	18.0555i	−0.650253	+	1.12627i	0.332808	+	0.942995i	$0.392004\pi$
$257$	−10.4244	+	18.0555i	−0.650253	+	1.12627i	−0.983061	+	0.183277i	$0.941329\pi$
$258$	−2.32336	−	2.66065i	−0.144646	−	0.165645i
$259$	2.66369	−	2.95833i	0.165514	−	0.183821i
$260$	0.432291	+	1.08107i	0.0268096	+	0.0670452i
$261$	−0.830012	+	6.10436i	−0.0513764	+	0.377850i
$262$	5.97377	+	18.3854i	0.369061	+	1.13585i
$263$	−6.07004	+	6.74146i	−0.374295	+	0.415696i	−0.900634	−	0.434578i	$-0.856897\pi$
$263$	−6.07004	+	6.74146i	−0.374295	+	0.415696i	0.526339	+	0.850275i	$0.323564\pi$
$264$	10.9912	−	11.8397i	0.676460	−	0.728683i
$265$	−1.31310	+	2.66799i	−0.0806629	+	0.163893i
$266$	15.5485	+	3.30493i	0.953338	+	0.202638i
$267$	4.23068	−	12.3769i	0.258914	−	0.757453i
$268$	5.45140	+	9.44209i	0.332997	+	0.576768i
$269$	12.0005	−	8.71886i	0.731683	−	0.531599i	−0.158413	−	0.987373i	$-0.550638\pi$
$269$	12.0005	−	8.71886i	0.731683	−	0.531599i	0.890095	+	0.455774i	$0.150638\pi$
$270$	−6.34978	−	18.2540i	−0.386435	−	1.11091i
$271$	6.34725	+	4.61155i	0.385568	+	0.280132i	0.763637	−	0.645646i	$-0.223412\pi$
$271$	6.34725	+	4.61155i	0.385568	+	0.280132i	−0.378069	+	0.925777i	$0.623412\pi$
$272$	1.10895	−	10.5510i	0.0672402	−	0.639748i
$273$	−0.480850	−	1.56027i	−0.0291024	−	0.0944316i
$274$	−13.7754	+	23.8597i	−0.832203	+	1.44142i
$275$	19.3670	−	11.9101i	1.16788	−	0.718208i
$276$	−0.129121	−	0.0598580i	−0.00777218	−	0.00360303i
$277$	21.7610	−	4.62545i	1.30749	−	0.277916i	0.499092	−	0.866549i	$-0.333667\pi$
$277$	21.7610	−	4.62545i	1.30749	−	0.277916i	0.808400	+	0.588633i	$0.200334\pi$
$278$	−22.6487	−	16.4552i	−1.35838	−	0.986919i
$279$	1.43999	+	19.3456i	0.0862100	+	1.15819i
$280$	−1.56255	+	6.17291i	−0.0933799	+	0.368902i
$281$	9.27859	+	4.13109i	0.553514	+	0.246440i	0.664380	−	0.747395i	$-0.268696\pi$
$281$	9.27859	+	4.13109i	0.553514	+	0.246440i	−0.110866	+	0.993835i	$0.535362\pi$
$282$	−3.04688	−	33.9491i	−0.181439	−	2.02164i
$283$	−0.0797346	−	0.758624i	−0.00473973	−	0.0450955i	0.991896	−	0.127049i	$-0.0405507\pi$
$283$	−0.0797346	−	0.758624i	−0.00473973	−	0.0450955i	−0.996636	+	0.0819538i	$0.973884\pi$
$284$	−10.1622	−	2.16005i	−0.603018	−	0.128175i
$285$	−18.8255	−	18.8758i	−1.11513	−	1.11811i
$286$	5.02339	−	1.06775i	0.297039	−	0.0631376i
$287$	−2.33074	−	7.17328i	−0.137579	−	0.423425i
$288$	−6.50947	+	10.5220i	−0.383574	+	0.620017i
$289$	−3.83131	+	11.7916i	−0.225371	+	0.693622i
$290$	7.34956	−	2.07904i	0.431581	−	0.122085i
$291$	−2.25292	+	18.6950i	−0.132069	+	1.09592i
$292$	0.474936	+	4.51872i	0.0277935	+	0.264438i
$293$	3.29507	−	5.70722i	0.192500	−	0.333419i	−0.753578	−	0.657358i	$-0.771674\pi$
$293$	3.29507	−	5.70722i	0.192500	−	0.333419i	0.946078	+	0.323939i	$0.105007\pi$
$294$	4.72700	−	13.8289i	0.275684	−	0.806516i
$295$	0.148994	−	3.86982i	0.00867476	−	0.225310i
$296$	4.75815	+	3.45699i	0.276562	+	0.200934i
$297$	−23.3118	+	3.85316i	−1.35269	+	0.223583i
$298$	−8.20364	+	25.2482i	−0.475224	+	1.46259i
$299$	0.0363745	+	0.0630025i	0.00210359	+	0.00364353i
$300$	−4.87941	+	4.50554i	−0.281713	+	0.260127i
$301$	0.851063	−	1.47408i	0.0490545	−	0.0849648i
$302$	−9.36656	−	10.4026i	−0.538985	−	0.598604i
$303$	−10.2970	−	18.4785i	−0.591548	−	1.06156i
$304$	−3.55840	+	33.8559i	−0.204088	+	1.94177i
$305$	−3.13418	−	7.83794i	−0.179462	−	0.448799i
$306$	−7.40145	+	7.73354i	−0.423113	+	0.442097i
$307$	20.2069			1.15327			0.576634	−	0.817002i	$-0.304366\pi$
$307$	20.2069			1.15327			0.576634	+	0.817002i	$0.304366\pi$
$308$	−4.42282	−	1.96917i	−0.252014	−	0.112204i
$309$	−1.35247	+	0.577674i	−0.0769396	+	0.0328627i
$310$	21.2765	−	11.2155i	1.20842	−	0.636997i
$311$	11.9608	+	13.2838i	0.678234	+	0.753255i	0.979754	−	0.200205i	$-0.0641608\pi$
$311$	11.9608	+	13.2838i	0.678234	+	0.753255i	−0.301520	+	0.953460i	$0.597494\pi$
$312$	2.21830	−	0.947489i	0.125587	−	0.0536410i
$313$	12.2784	−	13.6366i	0.694019	−	0.770786i	−0.288393	−	0.957512i	$-0.593121\pi$
$313$	12.2784	−	13.6366i	0.694019	−	0.770786i	0.982412	+	0.186726i	$0.0597877\pi$
$314$	0.0437675	−	0.134702i	0.00246994	−	0.00760170i
$315$	7.33367	−	5.74043i	0.413205	−	0.323437i
$316$	−2.12766	−	6.54826i	−0.119690	−	0.368369i
$317$	2.89860	+	1.29054i	0.162802	+	0.0724841i	0.486520	−	0.873670i	$-0.338266\pi$
$317$	2.89860	+	1.29054i	0.162802	+	0.0724841i	−0.323718	+	0.946154i	$0.604933\pi$
$318$	−3.47604	−	1.61142i	−0.194927	−	0.0903641i
$319$	−0.976064	−	9.28663i	−0.0546491	−	0.519952i
$320$	−6.70820	−	0.967250i	−0.375000	−	0.0540709i
$321$	33.0375	+	0.502571i	1.84398	+	0.0280508i
$322$	0.0258642	−	0.246082i	0.00144136	−	0.0137136i
$323$	−4.56282	+	14.0429i	−0.253882	+	0.781369i
$324$	6.46429	−	2.41869i	0.359127	−	0.134372i
$325$	3.36509	−	0.448416i	0.186662	−	0.0248736i
$326$	10.2602	+	17.7712i	0.568261	+	0.984256i
$327$	6.68585	+	21.6943i	0.369728	+	1.19970i
$328$	10.1800	−	4.53244i	0.562098	−	0.250262i
$329$	15.0050	−	6.68065i	0.827251	−	0.368316i
$330$	15.9222	+	24.5898i	0.876491	+	1.35363i
$331$	−13.4822	−	6.00268i	−0.741051	−	0.329937i	0.00125393	−	0.999999i	$-0.499601\pi$
$331$	−13.4822	−	6.00268i	−0.741051	−	0.329937i	−0.742305	+	0.670062i	$0.766268\pi$
$332$	13.9076			0.763278
$333$	−2.40811	−	8.25811i	−0.131963	−	0.452542i
$334$	3.44246	+	10.5948i	0.188363	+	0.579721i
$335$	30.5898	−	8.65322i	1.67130	−	0.472776i
$336$	−11.5937	−	2.64926i	−0.632491	−	0.144529i
$337$	11.9319	+	2.53619i	0.649970	+	0.138155i	0.521086	−	0.853504i	$-0.325527\pi$
$337$	11.9319	+	2.53619i	0.649970	+	0.138155i	0.128884	+	0.991660i	$0.458861\pi$
$338$	−20.4015	−	4.33648i	−1.10970	−	0.235873i
$339$	11.7573	+	2.68663i	0.638569	+	0.145918i
$340$	3.45213	+	1.27047i	0.187218	+	0.0689010i
$341$	−9.08639	−	27.9650i	−0.492056	−	1.51439i
$342$	23.7497	−	24.8153i	1.28424	−	1.34186i
$343$	16.7606			0.904989
$344$	2.29736	+	1.02285i	0.123865	+	0.0551485i
$345$	−0.261583	+	0.322149i	−0.0140832	+	0.0173439i
$346$	−17.4744	+	7.78011i	−0.939430	+	0.418261i
$347$	19.8592	−	8.84187i	1.06610	−	0.474656i	0.202730	−	0.979235i	$-0.435019\pi$
$347$	19.8592	−	8.84187i	1.06610	−	0.474656i	0.863366	+	0.504578i	$0.168352\pi$
$348$	0.803333	+	2.60666i	0.0430631	+	0.139732i
$349$	5.54554	+	9.60516i	0.296846	+	0.514152i	0.975413	−	0.220387i	$-0.0707319\pi$
$349$	5.54554	+	9.60516i	0.296846	+	0.514152i	−0.678567	+	0.734539i	$0.737399\pi$
$350$	−10.1561	−	5.49361i	−0.542866	−	0.293646i
$351$	−3.41387	−	0.890174i	−0.182219	−	0.0475140i
$352$	5.79531	−	17.8361i	0.308891	−	0.950669i
$353$	−0.530083	+	5.04340i	−0.0282135	+	0.268433i	0.971317	+	0.237789i	$0.0764226\pi$
$353$	−0.530083	+	5.04340i	−0.0282135	+	0.268433i	−0.999530	+	0.0306445i	$0.990244\pi$
$354$	4.98923	+	0.0758967i	0.265174	+	0.00403387i
$355$	−13.3768	+	27.1793i	−0.709965	+	1.44253i
$356$	−0.605357	−	5.75959i	−0.0320838	−	0.305257i
$357$	−4.67989	−	2.16951i	−0.247686	−	0.114822i
$358$	−7.46292	−	3.32271i	−0.394427	−	0.175610i
$359$	−9.46581	−	29.1328i	−0.499586	−	1.53757i	−0.809685	−	0.586864i	$-0.800362\pi$
$359$	−9.46581	−	29.1328i	−0.499586	−	1.53757i	0.310099	−	0.950704i	$-0.399638\pi$
$360$	9.56720	+	9.88913i	0.504236	+	0.521203i
$361$	8.76981	−	26.9907i	0.461569	−	1.42056i
$362$	−2.32737	+	2.58480i	−0.122324	+	0.135854i
$363$	15.4145	−	6.58388i	0.809049	−	0.345564i
$364$	−0.483707	−	0.537211i	−0.0253531	−	0.0281575i
$365$	13.1126	+	1.89069i	0.686342	+	0.0989632i
$366$	10.0022	−	4.27216i	0.522822	−	0.223310i
$367$	−14.5972	−	6.49910i	−0.761968	−	0.339250i	−0.0113057	−	0.999936i	$-0.503599\pi$
$367$	−14.5972	−	6.49910i	−0.761968	−	0.339250i	−0.750662	+	0.660686i	$0.770265\pi$
$368$	0.529910			0.0276235
$369$	−15.8317	−	3.87195i	−0.824163	−	0.201565i
$370$	−8.19434	+	6.82608i	−0.426003	+	0.354871i
$371$	0.192986	−	1.83614i	0.0100193	−	0.0953276i
$372$	4.18096	+	7.50293i	0.216773	+	0.389009i
$373$	7.53730	+	8.37102i	0.390267	+	0.433435i	0.905976	−	0.423328i	$-0.139138\pi$
$373$	7.53730	+	8.37102i	0.390267	+	0.433435i	−0.515710	+	0.856763i	$0.672472\pi$
$374$	8.11274	−	14.0517i	0.419500	−	0.726595i
$375$	9.24425	+	17.0160i	0.477371	+	0.878702i
$376$	12.1334	+	21.0157i	0.625733	+	1.08380i
$377$	0.430852	−	1.32603i	0.0221900	−	0.0682938i
$378$	7.61419	+	9.27448i	0.391632	+	0.477028i
$379$	−17.8996	−	13.0048i	−0.919440	−	0.668012i	0.0239446	−	0.999713i	$-0.492377\pi$
$379$	−17.8996	−	13.0048i	−0.919440	−	0.668012i	−0.943385	+	0.331701i	$0.892377\pi$
$380$	−11.0772	−	4.07668i	−0.568247	−	0.209129i
$381$	12.4302	−	36.3646i	0.636819	−	1.86302i
$382$	8.54123	−	14.7938i	0.437007	−	0.756919i
$383$	−0.661282	−	6.29168i	−0.0337899	−	0.321490i	−0.998340	−	0.0575909i	$-0.981658\pi$
$383$	−0.661282	−	6.29168i	−0.0337899	−	0.321490i	0.964550	−	0.263899i	$-0.0850086\pi$
$384$	2.75413	−	22.8542i	0.140546	−	1.16627i
$385$	−8.73065	+	11.0927i	−0.444955	+	0.565338i
$386$	0.903967	−	2.78213i	0.0460107	−	0.141606i
$387$	−1.74130	−	3.23978i	−0.0885154	−	0.164687i
$388$	2.57638	+	7.92927i	0.130796	+	0.402548i
$389$	−32.3577	+	6.87784i	−1.64060	+	0.348720i	−0.933551	−	0.358444i	$-0.883307\pi$
$389$	−32.3577	+	6.87784i	−1.64060	+	0.348720i	−0.707049	+	0.707165i	$0.749974\pi$
$390$	0.678501	+	4.32117i	0.0343572	+	0.218811i
$391$	0.224821	+	0.0477872i	0.0113697	+	0.00241670i
$392$	1.08758	+	10.3476i	0.0549309	+	0.522633i
$393$	1.79936	+	20.0489i	0.0907655	+	1.01133i
$394$	2.40786	+	1.07205i	0.121306	+	0.0540089i
$395$	−20.0319	+	1.32880i	−1.00791	+	0.0668591i
$396$	−8.64675	+	5.88890i	−0.434516	+	0.295928i
$397$	22.9141	+	16.6480i	1.15002	+	0.835541i	0.988484	−	0.151325i	$-0.0483539\pi$
$397$	22.9141	+	16.6480i	1.15002	+	0.835541i	0.161540	+	0.986866i	$0.448354\pi$
$398$	−7.87134	+	1.67310i	−0.394554	+	0.0838651i
$399$	15.0168	+	6.96149i	0.751779	+	0.348510i
$400$	9.42712	−	22.8608i	0.471356	−	1.14304i
$401$	−4.98614	+	8.63625i	−0.248996	+	0.431274i	−0.963248	−	0.268615i	$-0.913434\pi$
$401$	−4.98614	+	8.63625i	−0.248996	+	0.431274i	0.714251	+	0.699889i	$0.246767\pi$
$402$	12.0634	+	39.1436i	0.601670	+	1.95231i
$403$	0.458929	−	4.36642i	0.0228609	−	0.217507i
$404$	−7.57731	−	5.50524i	−0.376985	−	0.273896i
$405$	−2.21151	−	20.0027i	−0.109891	−	0.993944i
$406$	−3.83655	+	2.78742i	−0.190405	+	0.138337i
$407$	6.51926	+	11.2917i	0.323148	+	0.559708i
$408$	2.46501	−	7.21139i	0.122036	−	0.357017i
$409$	9.44969	+	2.00859i	0.467257	+	0.0993186i	0.435523	−	0.900178i	$-0.356564\pi$
$409$	9.44969	+	2.00859i	0.467257	+	0.0993186i	0.0317346	+	0.999496i	$0.489897\pi$
$410$	3.43772	+	19.9124i	0.169777	+	0.983402i
$411$	−19.5181	+	21.0249i	−0.962754	+	1.03708i
$412$	−0.435711	+	0.483906i	−0.0214659	+	0.0238403i
$413$	0.743021	+	2.28678i	0.0365617	+	0.112525i
$414$	−0.422806	−	0.327290i	−0.0207798	−	0.0160854i
$415$	9.95092	−	39.3116i	0.488471	−	1.92973i
$416$	1.87373	−	2.08099i	0.0918672	−	0.102029i
$417$	−19.1739	−	21.9574i	−0.938951	−	1.07526i
$418$	−26.0321	+	45.0889i	−1.27327	+	2.20537i
$419$	1.32174	+	12.5755i	0.0645710	+	0.614352i	0.978180	+	0.207758i	$0.0666168\pi$
$419$	1.32174	+	12.5755i	0.0645710	+	0.614352i	−0.913609	+	0.406594i	$0.866717\pi$
$420$	1.87693	−	3.67158i	0.0915850	−	0.179155i
$421$	2.39672	−	22.8033i	0.116809	−	1.11136i	−0.766393	−	0.642372i	$-0.777951\pi$
$421$	2.39672	−	22.8033i	0.116809	−	1.11136i	0.883202	−	0.468992i	$-0.155383\pi$
$422$	−5.77800	−	4.19797i	−0.281269	−	0.204354i
$423$	4.78191	−	35.1688i	0.232504	−	1.70996i
$424$	2.72771			0.132470
$425$	6.06116	−	8.84887i	0.294010	−	0.429233i
$426$	−35.4111	−	16.4159i	−1.71567	−	0.795352i
$427$	3.50695	+	3.89486i	0.169713	+	0.188485i
$428$	13.3647	−	5.95033i	0.646005	−	0.287620i
$429$	5.34696	+	0.0813386i	0.258154	+	0.00392706i
$430$	−2.82035	+	3.58340i	−0.136009	+	0.172807i
$431$	10.6124	−	7.71039i	0.511183	−	0.371397i	−0.302089	−	0.953280i	$-0.597684\pi$
$431$	10.6124	−	7.71039i	0.511183	−	0.371397i	0.813272	+	0.581883i	$0.197684\pi$
$432$	−18.0489	+	18.2933i	−0.868376	+	0.880138i
$433$	−19.0904	+	13.8700i	−0.917425	+	0.666548i	−0.942882	−	0.333128i	$-0.891896\pi$
$433$	−19.0904	+	13.8700i	−0.917425	+	0.666548i	0.0254569	+	0.999676i	$0.491896\pi$
$434$	−9.99217	+	11.0974i	−0.479639	+	0.532694i
$435$	7.94285	−	0.405647i	0.380831	−	0.0194493i
$436$	6.72557	+	7.46950i	0.322096	+	0.357724i
$437$	−0.721404	−	0.153339i	−0.0345094	−	0.00733521i
$438$	−2.04228	+	16.9471i	−0.0975840	+	0.809765i
$439$	7.92866	−	1.68529i	0.378414	−	0.0804344i	−0.0147778	−	0.999891i	$-0.504704\pi$
$439$	7.92866	−	1.68529i	0.378414	−	0.0804344i	0.393192	+	0.919456i	$0.371371\pi$
$440$	−17.6473	−	11.1152i	−0.841301	−	0.529896i
$441$	8.00617	−	12.9413i	0.381246	−	0.616254i
$442$	1.96001	−	1.42403i	0.0932280	−	0.0677341i
$443$	−0.254259	−	0.440389i	−0.0120802	−	0.0209235i	0.859922	−	0.510425i	$-0.170512\pi$
$443$	−0.254259	−	0.440389i	−0.0120802	−	0.0209235i	−0.872002	+	0.489502i	$0.837179\pi$
$444$	−2.50514	−	2.86882i	−0.118889	−	0.136148i
$445$	−16.7133	−	2.40988i	−0.792288	−	0.114239i
$446$	−24.6295	+	10.9658i	−1.16624	+	0.519244i
$447$	−14.1842	+	23.7268i	−0.670888	+	1.12224i
$448$	4.11609	−	0.874903i	0.194467	−	0.0413353i
$449$	7.22605			0.341018			0.170509	−	0.985356i	$-0.445459\pi$
$449$	7.22605			0.341018			0.170509	+	0.985356i	$0.445459\pi$
$450$	−21.6413	+	12.4178i	−1.02018	+	0.585380i
$451$	24.7040			1.16327
$452$	5.22317	−	1.11022i	0.245677	−	0.0522203i
$453$	−7.09509	−	12.7325i	−0.333356	−	0.598223i
$454$	−13.9985	+	6.23256i	−0.656984	+	0.292508i
$455$	−1.86459	+	0.982883i	−0.0874132	+	0.0460783i
$456$	−7.90969	+	23.1398i	−0.370405	+	1.08362i
$457$	−7.94049	−	13.7533i	−0.371441	−	0.643354i	0.618347	−	0.785905i	$-0.287803\pi$
$457$	−7.94049	−	13.7533i	−0.371441	−	0.643354i	−0.989787	+	0.142551i	$0.954469\pi$
$458$	−11.0413	+	8.02199i	−0.515927	+	0.374843i
$459$	−9.30715	+	6.13354i	−0.434421	+	0.286289i
$460$	−0.0450869	+	0.178118i	−0.00210219	+	0.00830478i
$461$	−32.2855	+	6.86249i	−1.50369	+	0.319618i	−0.884840	−	0.465895i	$-0.845733\pi$
$461$	−32.2855	+	6.86249i	−1.50369	+	0.319618i	−0.618845	+	0.785513i	$0.712399\pi$
$462$	−14.5504	−	10.9135i	−0.676947	−	0.507740i
$463$	−18.0119	−	3.82855i	−0.837084	−	0.177928i	−0.230625	−	0.973043i	$-0.574077\pi$
$463$	−18.0119	−	3.82855i	−0.837084	−	0.177928i	−0.606459	+	0.795115i	$0.707411\pi$
$464$	−6.79566	−	7.54734i	−0.315480	−	0.350377i
$465$	24.1995	−	6.44965i	1.12222	−	0.299096i
$466$	−9.22069	+	10.2406i	−0.427140	+	0.474387i
$467$	−14.9196	+	10.8397i	−0.690398	+	0.501603i	−0.876791	−	0.480872i	$-0.840320\pi$
$467$	−14.9196	+	10.8397i	−0.690398	+	0.501603i	0.186393	+	0.982475i	$0.440320\pi$
$468$	−1.53711	+	0.278147i	−0.0710528	+	0.0128574i
$469$	−15.9682	+	11.6016i	−0.737344	+	0.535712i
$470$	−42.3427	+	11.9779i	−1.95312	+	0.552498i
$471$	0.0756744	−	0.126585i	0.00348689	−	0.00583275i
$472$	−3.24531	+	1.44491i	−0.149378	+	0.0665072i
$473$	3.73043	+	4.14306i	0.171525	+	0.190498i
$474$	−2.31223	−	25.7634i	−0.106204	−	1.18335i
$475$	−19.4490	+	28.3942i	−0.892381	+	1.30281i
$476$	−2.28390			−0.104682
$477$	−3.15477	−	2.44207i	−0.144447	−	0.111815i
$478$	1.45226	+	1.05513i	0.0664250	+	0.0482606i
$479$	2.41271	−	22.9554i	0.110239	−	1.04886i	−0.789894	−	0.613243i	$-0.789865\pi$
$479$	2.41271	−	22.9554i	0.110239	−	1.04886i	0.900133	−	0.435614i	$-0.143469\pi$
$480$	14.9046	+	5.74417i	0.680301	+	0.262184i
$481$	0.203500	+	1.93617i	0.00927881	+	0.0882820i
$482$	−20.8726	+	36.1524i	−0.950720	+	1.64670i
$483$	0.0833362	−	0.243800i	0.00379193	−	0.0110933i
$484$	4.96589	−	5.51518i	0.225722	−	0.250690i
$485$	24.2565	−	1.60904i	1.10143	−	0.0730627i
$486$	25.6994	−	3.44839i	1.16575	−	0.156422i
$487$	−3.52725	−	10.8558i	−0.159835	−	0.491921i	0.838784	−	0.544465i	$-0.183267\pi$
$487$	−3.52725	−	10.8558i	−0.159835	−	0.491921i	−0.998619	+	0.0525435i	$0.983267\pi$
$488$	−5.18127	+	5.75439i	−0.234545	+	0.260489i
$489$	6.29302	+	20.4197i	0.284580	+	0.923409i
$490$	−18.6741	−	2.69260i	−0.843608	−	0.121639i
$491$	38.9241	+	8.27356i	1.75662	+	0.373381i	0.969818	−	0.243828i	$-0.0784033\pi$
$491$	38.9241	+	8.27356i	1.75662	+	0.373381i	0.786799	+	0.617209i	$0.211737\pi$
$492$	−7.08055	+	1.39280i	−0.319216	+	0.0627924i
$493$	−2.20253	−	3.81489i	−0.0991969	−	0.171814i
$494$	−6.28925	+	4.56941i	−0.282967	+	0.205587i
$495$	10.4590	+	28.6547i	0.470095	+	1.28793i
$496$	−25.8728	−	18.7977i	−1.16172	−	0.844041i
$497$	1.96599	−	18.7051i	0.0881866	−	0.839039i
$498$	50.9360	+	11.6393i	2.28250	+	0.521568i
$499$	18.1188	−	31.3826i	0.811107	−	1.40488i	−0.100983	−	0.994888i	$-0.532199\pi$
$499$	18.1188	−	31.3826i	0.811107	−	1.40488i	0.912090	−	0.409990i	$-0.134468\pi$
$500$	6.88208	+	5.11381i	0.307776	+	0.228697i
$501$	1.03690	+	11.5534i	0.0463253	+	0.516167i
$502$	−37.7312	+	8.02001i	−1.68403	+	0.357951i
$503$	26.1554	+	19.0030i	1.16621	+	0.847302i	0.990550	−	0.137149i	$-0.0437939\pi$
$503$	26.1554	+	19.0030i	1.16621	+	0.847302i	0.175661	+	0.984451i	$0.443794\pi$
$504$	−7.69514	−	3.71055i	−0.342769	−	0.165281i
$505$	−20.9829	+	17.4792i	−0.933725	+	0.777816i
$506$	0.740374	+	0.329636i	0.0329136	+	0.0146541i
$507$	−19.7039	−	9.13434i	−0.875081	−	0.405670i
$508$	−1.77860	−	16.9223i	−0.0789128	−	0.750805i
$509$	0.264168	+	0.0561506i	0.0117090	+	0.00248883i	0.213762	−	0.976886i	$-0.431428\pi$
$509$	0.264168	+	0.0561506i	0.0117090	+	0.00248883i	−0.202053	+	0.979374i	$0.564761\pi$
$510$	11.5801	+	7.54215i	0.512774	+	0.333972i
$511$	−8.04575	+	1.71018i	−0.355923	+	0.0756538i
$512$	−0.0335504	−	0.103257i	−0.00148273	−	0.00456337i
$513$	29.8647	−	19.6812i	1.31856	−	0.868948i
$514$	−10.7166	+	32.9823i	−0.472689	+	1.45479i
$515$	1.05607	+	1.57783i	0.0465360	+	0.0695274i
$516$	−1.30278	−	0.977145i	−0.0573518	−	0.0430164i
$517$	5.62336	+	53.5027i	0.247315	+	2.35304i
$518$	3.31084	−	5.73454i	0.145470	−	0.251961i
$519$	−19.5431	+	3.84429i	−0.857847	+	0.168746i
$520$	−1.73214	−	2.58792i	−0.0759595	−	0.113488i
$521$	22.4017	+	16.2758i	0.981435	+	0.713054i	0.958029	−	0.286672i	$-0.0925489\pi$
$521$	22.4017	+	16.2758i	0.981435	+	0.713054i	0.0234061	+	0.999726i	$0.492549\pi$
$522$	0.760659	+	10.2191i	0.0332931	+	0.447279i
$523$	11.9194	−	36.6841i	0.521198	−	1.60408i	−0.250515	−	0.968113i	$-0.580600\pi$
$523$	11.9194	−	36.6841i	0.521198	−	1.60408i	0.771713	−	0.635971i	$-0.219400\pi$
$524$	4.45627	+	7.71848i	0.194673	+	0.337183i
$525$	−9.03523	−	7.93242i	−0.394330	−	0.346199i
$526$	−7.54477	+	13.0679i	−0.328968	+	0.569789i
$527$	−9.28170	−	10.3084i	−0.404317	−	0.449040i
$528$	19.9869	−	33.4335i	0.869820	−	1.45500i
$529$	2.40295	−	22.8626i	0.104476	−	0.994025i
$530$	−1.21377	+	4.79506i	−0.0527229	+	0.208284i
$531$	5.04701	+	1.23435i	0.219021	+	0.0535660i
$532$	7.32855			0.317733
$533$	3.36976	+	1.50032i	0.145961	+	0.0649859i
$534$	2.60310	−	21.6009i	0.112647	−	0.934763i
$535$	−7.25691	−	42.0344i	−0.313744	−	1.81731i
$536$	−19.5127	−	21.6711i	−0.842820	−	0.936047i
$537$	−6.80494	−	5.10401i	−0.293655	−	0.220254i
$538$	16.5100	−	18.3362i	0.711798	−	0.790531i
$539$	−7.12781	+	21.9371i	−0.307016	+	0.944900i
$540$	−4.61324	−	7.62320i	−0.198522	−	0.328050i
$541$	−9.26487	−	28.5143i	−0.398328	−	1.22593i	−0.926339	−	0.376690i	$-0.877062\pi$
$541$	−9.26487	−	28.5143i	−0.398328	−	1.22593i	0.528011	−	0.849237i	$-0.322938\pi$
$542$	11.9221	+	5.30808i	0.512099	+	0.228001i
$543$	−2.96210	+	2.08400i	−0.127116	+	0.0894331i
$544$	−0.924776	−	8.79865i	−0.0396494	−	0.377239i
$545$	25.9257	−	13.6662i	1.11053	−	0.585397i
$546$	−1.32197	−	2.37233i	−0.0565749	−	0.101526i
$547$	−0.600529	+	5.71365i	−0.0256768	+	0.244298i	0.974154	+	0.225886i	$0.0725277\pi$
$547$	−0.600529	+	5.71365i	−0.0256768	+	0.244298i	−0.999830	+	0.0184119i	$0.994139\pi$
$548$	−3.92511	+	12.0802i	−0.167672	+	0.516042i
$549$	11.1443	−	2.01661i	0.475626	−	0.0860667i
$550$	27.3921	−	26.0762i	1.16800	−	1.11189i
$551$	7.06745	+	12.2412i	0.301083	+	0.521492i
$552$	0.371095	+	0.0847980i	0.0157949	+	0.00360924i
$553$	11.3870	−	5.06984i	0.484227	−	0.215592i
$554$	33.8065	−	15.0516i	1.43630	−	0.639483i
$555$	−9.90152	+	5.02846i	−0.420296	+	0.213446i
$556$	−11.7910	−	5.24969i	−0.500049	−	0.222636i
$557$	−13.8510			−0.586887			−0.293444	−	0.955976i	$-0.594801\pi$
$557$	−13.8510			−0.586887			−0.293444	+	0.955976i	$0.594801\pi$
$558$	9.03342	+	30.9783i	0.382415	+	1.31141i
$559$	0.257236	+	0.791691i	0.0108799	+	0.0334850i
$560$	−0.590686	+	15.3419i	−0.0249610	+	0.648313i
$561$	11.4947	−	12.3822i	0.485309	−	0.522775i
$562$	16.5254	+	3.51258i	0.697081	+	0.148169i
$563$	29.1494	+	6.19591i	1.22850	+	0.261126i	0.776055	−	0.630665i	$-0.217218\pi$
$563$	29.1494	+	6.19591i	1.22850	+	0.261126i	0.452447	+	0.891791i	$0.350551\pi$
$564$	−4.62820	−	15.0176i	−0.194883	−	0.632357i
$565$	0.599018	−	15.5583i	0.0252009	−	0.654543i
$566$	−0.392094	−	1.20674i	−0.0164809	−	0.0507231i
$567$	5.57793	+	11.1808i	0.234251	+	0.469549i
$568$	27.7878			1.16595
$569$	14.9654	+	6.66301i	0.627381	+	0.279328i	0.695696	−	0.718336i	$-0.255096\pi$
$569$	14.9654	+	6.66301i	0.627381	+	0.279328i	−0.0683159	+	0.997664i	$0.521763\pi$
$570$	−37.1580	−	24.2012i	−1.55638	−	1.01368i
$571$	−4.71944	+	2.10123i	−0.197502	+	0.0879337i	−0.503104	−	0.864226i	$-0.667809\pi$
$571$	−4.71944	+	2.10123i	−0.197502	+	0.0879337i	0.305602	+	0.952159i	$0.401142\pi$
$572$	2.16300	−	0.963031i	0.0904397	−	0.0402663i
$573$	12.1019	−	13.0361i	0.505562	−	0.544592i
$574$	−6.27303	−	10.8652i	−0.261831	−	0.453505i
$575$	0.471213	+	0.254888i	0.0196509	+	0.0106295i
$576$	3.07166	−	8.55855i	0.127986	−	0.356606i
$577$	4.99821	−	15.3829i	0.208078	−	0.640399i	−0.791495	−	0.611176i	$-0.790697\pi$
$577$	4.99821	−	15.3829i	0.208078	−	0.640399i	0.999573	−	0.0292230i	$-0.00930328\pi$
$578$	−2.15574	+	20.5105i	−0.0896668	+	0.853122i
$579$	1.56297	−	2.61448i	0.0649547	−	0.108654i
$580$	3.11508	−	1.64206i	0.129347	−	0.0681826i
$581$	2.63177	+	25.0396i	0.109184	+	1.03882i
$582$	2.79988	+	31.1969i	0.116059	+	1.29315i
$583$	5.52430	+	2.45958i	0.228793	+	0.101865i
$584$	−3.75536	−	11.5578i	−0.155398	−	0.478266i
$585$	−0.313587	+	4.54385i	−0.0129652	+	0.187865i
$586$	3.38744	−	10.4255i	0.139934	−	0.430672i
$587$	−18.8057	+	20.8858i	−0.776193	+	0.862050i	−0.993474	−	0.114059i	$-0.963615\pi$
$587$	−18.8057	+	20.8858i	−0.776193	+	0.862050i	0.217281	+	0.976109i	$0.430281\pi$
$588$	0.806132	−	6.68939i	0.0332443	−	0.275866i
$589$	29.7830	+	33.0774i	1.22719	+	1.36293i
$590$	−1.09592	−	6.34790i	−0.0451182	−	0.261339i
$591$	2.19556	+	1.64677i	0.0903135	+	0.0677391i
$592$	12.9549	+	5.76791i	0.532444	+	0.237060i
$593$	3.80524			0.156262			0.0781312	−	0.996943i	$-0.475105\pi$
$593$	3.80524			0.156262			0.0781312	+	0.996943i	$0.475105\pi$
$594$	−36.5969	+	14.3314i	−1.50159	+	0.588025i
$595$	−1.63414	+	6.45573i	−0.0669931	+	0.264659i
$596$	−1.27936	+	12.1723i	−0.0524047	+	0.498597i
$597$	−8.37836	−	0.127453i	−0.342903	−	0.00521629i
$598$	0.0809718	+	0.0899283i	0.00331118	+	0.00367744i
$599$	17.5681	−	30.4289i	0.717813	−	1.24329i	−0.244051	−	0.969762i	$-0.578476\pi$
$599$	17.5681	−	30.4289i	0.717813	−	1.24329i	0.961864	−	0.273527i	$-0.0881902\pi$
$600$	10.2601	−	14.5009i	0.418866	−	0.591995i
$601$	−10.6092	−	18.3758i	−0.432760	−	0.749563i	0.564350	−	0.825536i	$-0.309127\pi$
$601$	−10.6092	−	18.3758i	−0.432760	−	0.749563i	−0.997110	+	0.0759732i	$0.975794\pi$
$602$	0.874923	−	2.69274i	0.0356592	−	0.109748i
$603$	3.16596	+	42.5333i	0.128928	+	1.73209i
$604$	−5.22110	−	3.79335i	−0.212443	−	0.154349i
$605$	−12.0363	−	17.9829i	−0.489343	−	0.731107i
$606$	−23.1443	−	26.5042i	−0.940173	−	1.07666i
$607$	−7.55362	+	13.0833i	−0.306592	+	0.531033i	−0.977615	−	0.210404i	$-0.932522\pi$
$607$	−7.55362	+	13.0833i	−0.306592	+	0.531033i	0.671023	+	0.741437i	$0.265855\pi$
$608$	2.96741	+	28.2330i	0.120344	+	1.14500i
$609$	−4.54109	+	1.93961i	−0.184014	+	0.0785969i
$610$	−7.81012	−	11.6688i	−0.316222	−	0.472454i
$611$	−2.48225	+	7.63958i	−0.100421	+	0.309064i
$612$	−2.59647	+	4.19699i	−0.104956	+	0.169653i
$613$	−0.267857	−	0.824379i	−0.0108186	−	0.0332963i	0.945501	−	0.325618i	$-0.105572\pi$
$613$	−0.267857	−	0.824379i	−0.0108186	−	0.0332963i	−0.956320	+	0.292321i	$0.905572\pi$
$614$	32.8776	−	6.98834i	1.32683	−	0.282026i
$615$	−1.12922	+	21.0106i	−0.0455345	+	0.847231i
$616$	12.6661	+	2.69226i	0.510331	+	0.108474i
$617$	−2.07726	−	19.7638i	−0.0836272	−	0.795660i	−0.953299	−	0.302029i	$-0.902336\pi$
$617$	−2.07726	−	19.7638i	−0.0836272	−	0.795660i	0.869671	−	0.493631i	$-0.164331\pi$
$618$	−2.00076	+	1.40764i	−0.0804823	+	0.0566237i
$619$	16.3619	+	7.28480i	0.657641	+	0.292801i	0.708296	−	0.705915i	$-0.249464\pi$
$619$	16.3619	+	7.28480i	0.657641	+	0.292801i	−0.0506549	+	0.998716i	$0.516131\pi$
$620$	8.51980	−	7.09720i	0.342163	−	0.285030i
$621$	−0.353276	−	0.430309i	−0.0141765	−	0.0172677i
$622$	24.0548	+	17.4768i	0.964510	+	0.700757i
$623$	10.2552	−	2.17980i	0.410864	−	0.0873319i
$624$	4.75680	−	3.34667i	0.190424	−	0.133974i
$625$	19.3790	−	15.7941i	0.775160	−	0.631765i
$626$	15.2615	−	26.4337i	0.609973	−	1.05650i
$627$	−36.8842	+	39.7317i	−1.47301	+	1.58673i
$628$	0.00682556	−	0.0649409i	0.000272370	−	0.00259142i
$629$	4.97615	+	3.61538i	0.198412	+	0.144155i
$630$	9.94695	−	11.8762i	0.396296	−	0.473160i
$631$	−27.5034	+	19.9824i	−1.09489	+	0.795487i	−0.980219	−	0.197916i	$-0.936583\pi$
$631$	−27.5034	+	19.9824i	−1.09489	+	0.795487i	−0.114675	+	0.993403i	$0.536583\pi$
$632$	9.20786	+	15.9485i	0.366269	+	0.634396i
$633$	−4.89154	−	5.60166i	−0.194421	−	0.222646i
$634$	5.16248	+	1.09732i	0.205028	+	0.0435801i
$635$	−49.1056	−	7.08050i	−1.94870	−	0.280981i
$636$	−1.72202	−	0.393495i	−0.0682826	−	0.0156031i
$637$	−2.30455	+	2.55946i	−0.0913097	+	0.101410i
$638$	−4.79979	−	14.7722i	−0.190025	−	0.584838i
$639$	−32.1383	−	24.8779i	−1.27137	−	0.984154i
$640$	−29.6529	+	1.96701i	−1.17213	+	0.0777527i
$641$	−8.52288	+	9.46562i	−0.336634	+	0.373870i	−0.887566	−	0.460680i	$-0.847606\pi$
$641$	−8.52288	+	9.46562i	−0.336634	+	0.373870i	0.550932	+	0.834550i	$0.314272\pi$
$642$	53.9274	−	10.6080i	2.12835	−	0.418664i
$643$	9.31365	−	16.1317i	0.367295	−	0.636173i	−0.621847	−	0.783139i	$-0.713617\pi$
$643$	9.31365	−	16.1317i	0.367295	−	0.636173i	0.989142	+	0.146966i	$0.0469507\pi$
$644$	−0.0119243	−	0.113453i	−0.000469885	−	0.00447066i
$645$	−3.69417	+	2.98333i	−0.145458	+	0.117469i
$646$	−2.56733	+	24.4265i	−0.101010	+	0.961047i
$647$	−2.58476	−	1.87794i	−0.101617	−	0.0738294i	0.535816	−	0.844335i	$-0.320004\pi$
$647$	−2.58476	−	1.87794i	−0.101617	−	0.0738294i	−0.637434	+	0.770505i	$0.720004\pi$
$648$	−15.5670	+	9.92256i	−0.611528	+	0.389795i
$649$	−7.87544			−0.309138
$650$	5.32009	−	1.89338i	0.208671	−	0.0742643i
$651$	−12.7173	+	8.94731i	−0.498430	+	0.350673i
$652$	6.33041	+	7.03063i	0.247918	+	0.275341i
$653$	−4.61992	+	2.05692i	−0.180792	+	0.0804936i	−0.495136	−	0.868815i	$-0.664882\pi$
$653$	−4.61992	+	2.05692i	−0.180792	+	0.0804936i	0.314345	+	0.949309i	$0.398215\pi$
$654$	18.3809	+	32.9854i	0.718751	+	1.28983i
$655$	25.0057	−	7.07361i	0.977055	−	0.276389i
$656$	21.7371	−	15.7929i	0.848691	−	0.616610i
$657$	−6.00419	+	16.7294i	−0.234246	+	0.652678i
$658$	22.1034	−	16.0590i	0.861679	−	0.626046i
$659$	0.955484	−	1.06117i	0.0372204	−	0.0413374i	−0.724247	−	0.689540i	$-0.757813\pi$
$659$	0.955484	−	1.06117i	0.0372204	−	0.0413374i	0.761468	+	0.648203i	$0.224479\pi$
$660$	9.53736	+	9.56283i	0.371241	+	0.372233i
$661$	−3.11002	−	3.45402i	−0.120966	−	0.134346i	0.679620	−	0.733564i	$-0.262145\pi$
$661$	−3.11002	−	3.45402i	−0.120966	−	0.134346i	−0.800586	+	0.599219i	$0.795478\pi$
$662$	−24.0122	−	5.10395i	−0.933261	−	0.198371i
$663$	2.31994	−	0.990900i	0.0900989	−	0.0384834i
$664$	−36.3852	+	7.73391i	−1.41202	+	0.300134i
$665$	5.24360	−	20.7151i	0.203338	−	0.803296i
$666$	−6.77408	−	12.6035i	−0.262490	−	0.488376i
$667$	0.178005	−	0.129328i	0.00689238	−	0.00500761i
$668$	2.56797	+	4.44786i	0.0993579	+	0.172093i
$669$	−27.5453	+	5.41838i	−1.06496	+	0.209487i
$670$	46.7784	−	24.6583i	1.80721	−	0.952635i
$671$	−15.6821	+	6.98212i	−0.605401	+	0.269542i
$672$	−9.91628	−	0.150848i	−0.382529	−	0.00581907i
$673$	−18.4133	+	3.91386i	−0.709780	+	0.150868i	−0.548634	−	0.836062i	$-0.684852\pi$
$673$	−18.4133	+	3.91386i	−0.709780	+	0.150868i	−0.161145	+	0.986931i	$0.551519\pi$
$674$	20.2908			0.781572
$675$	−24.8488	+	7.58549i	−0.956429	+	0.291965i
$676$	−9.61597			−0.369845
$677$	9.69731	−	2.06123i	0.372698	−	0.0792194i	−0.0177547	−	0.999842i	$-0.505652\pi$
$677$	9.69731	−	2.06123i	0.372698	−	0.0792194i	0.390453	+	0.920623i	$0.372318\pi$
$678$	20.0588	+	0.305137i	0.770354	+	0.0117187i
$679$	−13.7885	+	6.13906i	−0.529156	+	0.235595i
$680$	−9.73802	−	1.40412i	−0.373436	−	0.0538454i
$681$	−15.6558	+	3.07962i	−0.599930	+	0.118011i
$682$	−24.4554	−	42.3580i	−0.936445	−	1.62197i
$683$	21.4995	−	15.6203i	0.822655	−	0.597694i	−0.0948166	−	0.995495i	$-0.530226\pi$
$683$	21.4995	−	15.6203i	0.822655	−	0.597694i	0.917472	+	0.397801i	$0.130226\pi$
$684$	8.33153	−	13.4673i	0.318564	−	0.514933i
$685$	31.3379	+	19.7383i	1.19736	+	0.754161i
$686$	27.2703	−	5.79649i	1.04119	−	0.221311i
$687$	−13.0689	+	5.58205i	−0.498611	+	0.212968i
$688$	5.93101	+	1.26068i	0.226118	+	0.0480628i
$689$	0.604171	+	0.671000i	0.0230171	+	0.0255631i
$690$	−0.314196	+	0.614617i	−0.0119612	+	0.0233981i
$691$	−22.2009	+	24.6566i	−0.844563	+	0.937982i	−0.998746	−	0.0500602i	$-0.984059\pi$
$691$	−22.2009	+	24.6566i	−0.844563	+	0.937982i	0.154183	+	0.988042i	$0.450725\pi$
$692$	−7.13452	+	5.18353i	−0.271214	+	0.197048i
$693$	−12.2388	−	14.4535i	−0.464913	−	0.549042i
$694$	29.2539	−	21.2542i	1.11046	−	0.806799i
$695$	−23.2754	+	29.5726i	−0.882886	+	1.12175i
$696$	−3.55124	−	6.37286i	−0.134609	−	0.241563i
$697$	10.6465	−	4.74011i	0.403263	−	0.179544i
$698$	12.3447	+	13.7102i	0.467253	+	0.518938i
$699$	−11.7354	+	8.25650i	−0.443874	+	0.312290i
$700$	−5.10659	−	1.50390i	−0.193011	−	0.0568419i
$701$	26.1441			0.987451			0.493725	−	0.869618i	$-0.335635\pi$
$701$	26.1441			0.987451			0.493725	+	0.869618i	$0.335635\pi$
$702$	−5.86239	−	0.267703i	−0.221261	−	0.0101038i
$703$	−15.9674	−	11.6010i	−0.602223	−	0.437540i
$704$	−1.44069	+	13.7073i	−0.0542981	+	0.516612i
$705$	−45.7608	+	2.33703i	−1.72345	+	0.0880178i
$706$	0.881738	+	8.38918i	0.0331846	+	0.315731i
$707$	8.47791	−	14.6842i	0.318845	−	0.552255i
$708$	2.25722	−	0.444015i	0.0848316	−	0.0166871i
$709$	26.7119	−	29.6666i	1.00319	−	1.11415i	0.00973033	−	0.999953i	$-0.496903\pi$
$709$	26.7119	−	29.6666i	1.00319	−	1.11415i	0.993458	−	0.114201i	$-0.0364306\pi$
$710$	−12.3649	+	48.8483i	−0.464048	+	1.83324i
$711$	3.62892	−	26.6890i	0.136095	−	1.00092i
$712$	4.78661	+	14.7317i	0.179386	+	0.552093i
$713$	0.463608	−	0.514888i	0.0173622	−	0.0192827i
$714$	−8.36470	−	1.91140i	−0.313041	−	0.0715322i
$715$	−1.17449	−	6.80306i	−0.0439236	−	0.254420i
$716$	−3.68398	−	0.783055i	−0.137677	−	0.0292641i
$717$	1.22946	+	1.40794i	0.0459149	+	0.0525805i
$718$	−25.4766	−	44.1267i	−0.950777	−	1.64679i
$719$	32.4317	−	23.5630i	1.20950	−	0.878751i	0.214312	−	0.976765i	$-0.431249\pi$
$719$	32.4317	−	23.5630i	1.20950	−	0.878751i	0.995185	+	0.0980142i	$0.0312491\pi$
$720$	27.5214	+	18.5270i	1.02566	+	0.690462i
$721$	−0.953688	−	0.692895i	−0.0355172	−	0.0258048i
$722$	4.93444	−	46.9481i	0.183641	−	1.74723i
$723$	−29.5739	+	31.8570i	−1.09986	+	1.18477i
$724$	−0.801787	+	1.38874i	−0.0297982	+	0.0516120i
$725$	−2.41263	−	9.98006i	−0.0896029	−	0.370650i
$726$	22.8031	−	16.0432i	0.846301	−	0.595419i
$727$	34.5304	−	7.33967i	1.28066	−	0.272213i	0.483162	−	0.875531i	$-0.339488\pi$
$727$	34.5304	−	7.33967i	1.28066	−	0.272213i	0.797501	+	0.603318i	$0.206155\pi$
$728$	1.56422	+	1.13647i	0.0579738	+	0.0421204i
$729$	26.8876	+	2.46075i	0.995838	+	0.0911390i
$730$	21.9886	−	1.45860i	0.813835	−	0.0539852i
$731$	2.40262	+	1.06972i	0.0888641	+	0.0395649i
$732$	4.10108	−	2.88534i	0.151580	−	0.106645i
$733$	−0.702668	−	6.68544i	−0.0259536	−	0.246932i	−0.999805	−	0.0197463i	$-0.993714\pi$
$733$	−0.702668	−	6.68544i	−0.0259536	−	0.246932i	0.973851	−	0.227186i	$-0.0729525\pi$
$734$	−25.9980	−	5.52604i	−0.959603	−	0.203970i
$735$	−18.3316	−	7.06491i	−0.676172	−	0.260593i
$736$	0.432244	−	0.0918764i	0.0159327	−	0.00338661i
$737$	−19.9773	−	61.4839i	−0.735874	−	2.26479i
$738$	−27.0979	−	0.824624i	−0.997488	−	0.0303548i
$739$	−3.30815	+	10.1814i	−0.121692	+	0.374530i	−0.993284	−	0.115702i	$-0.963088\pi$
$739$	−3.30815	+	10.1814i	−0.121692	+	0.374530i	0.871592	+	0.490233i	$0.163088\pi$
$740$	−3.04102	+	3.86376i	−0.111790	+	0.142035i
$741$	−7.44419	+	3.17959i	−0.273469	+	0.116805i
$742$	−0.321012	−	3.05423i	−0.0117847	−	0.112124i
$743$	−10.6028	+	18.3647i	−0.388981	+	0.673735i	−0.992313	−	0.123756i	$-0.960506\pi$
$743$	−10.6028	+	18.3647i	−0.388981	+	0.673735i	0.603332	+	0.797490i	$0.293839\pi$
$744$	−15.1106	−	17.3043i	−0.553982	−	0.634405i
$745$	33.4912	+	12.3256i	1.22702	+	0.451575i
$746$	15.1586	+	11.0133i	0.554995	+	0.403227i
$747$	49.0058	+	23.6303i	1.79303	+	0.864586i
$748$	2.31161	−	7.11441i	0.0845209	−	0.260129i
$749$	13.2422	+	22.9361i	0.483858	+	0.838067i
$750$	20.9256	+	24.4888i	0.764096	+	0.894204i
$751$	−24.6961	+	42.7750i	−0.901175	+	1.56088i	−0.0752042	+	0.997168i	$0.523961\pi$
$751$	−24.6961	+	42.7750i	−0.901175	+	1.56088i	−0.825971	+	0.563713i	$0.809372\pi$
$752$	39.1515	+	43.4822i	1.42771	+	1.58563i
$753$	−40.1616	−	0.610943i	−1.46357	−	0.0222640i
$754$	0.242424	−	2.30651i	0.00882857	−	0.0839982i
$755$	−14.4581	+	12.0439i	−0.526184	+	0.438324i
$756$	4.32271	+	3.45257i	0.157215	+	0.125569i
$757$	−31.2549			−1.13598			−0.567989	−	0.823036i	$-0.692279\pi$
$757$	−31.2549			−1.13598			−0.567989	+	0.823036i	$0.692279\pi$
$758$	−33.6210	−	14.9690i	−1.22117	−	0.543700i
$759$	0.675098	+	0.506353i	0.0245045	+	0.0183795i
$760$	31.2473	+	4.50552i	1.13346	+	0.163432i
$761$	−19.3977	−	21.5434i	−0.703168	−	0.780947i	0.280709	−	0.959793i	$-0.409430\pi$
$761$	−19.3977	−	21.5434i	−0.703168	−	0.780947i	−0.983877	+	0.178846i	$0.942764\pi$
$762$	7.64820	−	63.4658i	0.277065	−	2.29912i
$763$	−12.1756	+	13.5224i	−0.440786	+	0.489543i
$764$	2.43370	−	7.49016i	0.0880482	−	0.270985i
$765$	10.0055	+	10.3422i	0.361751	+	0.373924i
$766$	−3.25185	−	10.0082i	−0.117494	−	0.361610i
$767$	−1.07425	−	0.478289i	−0.0387891	−	0.0172700i
$768$	−2.48420	−	27.6796i	−0.0896409	−	0.998800i
$769$	−3.56272	−	33.8970i	−0.128475	−	1.22236i	−0.848797	−	0.528719i	$-0.822673\pi$
$769$	−3.56272	−	33.8970i	−0.128475	−	1.22236i	0.720322	−	0.693640i	$-0.243994\pi$
$770$	−10.3689	+	21.0678i	−0.373668	+	0.759230i
$771$	−18.5291	+	30.9948i	−0.667309	+	1.11625i
$772$	0.140974	−	1.34128i	0.00507377	−	0.0482737i
$773$	−9.44334	+	29.0636i	−0.339653	+	1.04535i	0.624731	+	0.780840i	$0.285209\pi$
$773$	−9.44334	+	29.0636i	−0.339653	+	1.04535i	−0.964384	+	0.264506i	$0.914791\pi$
$774$	−3.95362	−	4.66906i	−0.142110	−	0.167826i
$775$	−13.9652	−	29.1604i	−0.501645	−	1.04747i
$776$	−11.1498	−	19.3120i	−0.400253	−	0.693259i
$777$	4.69105	−	5.05320i	0.168290	−	0.181283i
$778$	−50.2688	+	22.3811i	−1.80223	+	0.802402i
$779$	−34.1622	+	15.2100i	−1.22399	+	0.544955i
$780$	0.720183	+	1.88364i	0.0257867	+	0.0674453i
$781$	56.2771	+	25.0562i	2.01375	+	0.896581i
$782$	0.382321			0.0136718
$783$	−1.59828	+	10.5500i	−0.0571177	+	0.377025i
$784$	7.75234	+	23.8592i	0.276869	+	0.852116i
$785$	−0.178680	−	0.0657588i	−0.00637736	−	0.00234703i
$786$	9.86132	+	31.9981i	0.351742	+	1.14134i
$787$	22.4498	+	4.77185i	0.800249	+	0.170098i	0.589845	−	0.807517i	$-0.299189\pi$
$787$	22.4498	+	4.77185i	0.800249	+	0.170098i	0.210404	+	0.977615i	$0.432522\pi$
$788$	1.18861	+	0.252647i	0.0423425	+	0.00900017i
$789$	−10.6900	+	11.5153i	−0.380574	+	0.409955i
$790$	−32.1332	+	9.08982i	−1.14325	+	0.323401i
$791$	2.98726	+	9.19384i	0.106215	+	0.326895i
$792$	19.3470	−	20.2150i	0.687465	−	0.718310i
$793$	−2.56316			−0.0910205
$794$	43.0398	+	19.1626i	1.52743	+	0.680054i
$795$	−2.34437	+	4.58597i	−0.0831464	+	0.162647i
$796$	−3.38929	+	1.50901i	−0.120130	+	0.0534854i
$797$	39.7228	−	17.6857i	1.40705	−	0.626461i	0.444063	−	0.895996i	$-0.353537\pi$
$797$	39.7228	−	17.6857i	1.40705	−	0.626461i	0.962991	+	0.269535i	$0.0868699\pi$
$798$	26.8406	+	6.13327i	0.950145	+	0.217115i
$799$	12.6893	+	21.9786i	0.448916	+	0.777545i
$800$	3.72601	−	20.2819i	0.131734	−	0.717075i
$801$	7.65298	−	21.3235i	0.270405	−	0.753427i
$802$	−5.12593	+	15.7760i	−0.181003	+	0.557070i
$803$	2.81613	−	26.7937i	0.0993790	−	0.945528i
$804$	9.19225	+	16.4959i	0.324186	+	0.581766i
$805$	−0.329220	−	0.0474700i	−0.0116035	−	0.00167310i
$806$	−0.763381	−	7.26308i	−0.0268889	−	0.255831i
$807$	21.0127	−	14.7836i	0.739684	−	0.520408i
$808$	22.8853	+	10.1892i	0.805102	+	0.358455i
$809$	−8.36599	−	25.7479i	−0.294133	−	0.905247i	−0.983511	−	0.180846i	$-0.942116\pi$
$809$	−8.36599	−	25.7479i	−0.294133	−	0.905247i	0.689379	−	0.724401i	$-0.257884\pi$
$810$	−10.5160	−	31.7805i	−0.369493	−	1.11665i
$811$	−11.3390	+	34.8979i	−0.398167	+	1.22543i	0.528300	+	0.849058i	$0.322829\pi$
$811$	−11.3390	+	34.8979i	−0.398167	+	1.22543i	−0.926468	+	0.376375i	$0.877171\pi$
$812$	−1.46295	+	1.62477i	−0.0513395	+	0.0570182i
$813$	10.8710	+	8.15373i	0.381263	+	0.285964i
$814$	14.5122	+	16.1175i	0.508654	+	0.564918i
$815$	24.4024	−	12.8633i	0.854779	−	0.450581i
$816$	2.19851	−	18.2435i	0.0769632	−	0.638651i
$817$	−7.70951	−	3.43249i	−0.269721	−	0.120088i
$818$	16.0697			0.561865
$819$	−0.791654	−	2.71482i	−0.0276626	−	0.0948634i
$820$	3.45897	+	8.65018i	0.120793	+	0.302078i
$821$	−0.158330	+	1.50641i	−0.00552576	+	0.0525741i	−0.996937	−	0.0782049i	$-0.975081\pi$
$821$	−0.158330	+	1.50641i	−0.00552576	+	0.0525741i	0.991412	+	0.130779i	$0.0417478\pi$
$822$	−24.4855	+	40.9586i	−0.854031	+	1.42859i
$823$	−24.3576	−	27.0519i	−0.849053	−	0.942969i	0.149900	−	0.988701i	$-0.452105\pi$
$823$	−24.3576	−	27.0519i	−0.849053	−	0.942969i	−0.998954	+	0.0457319i	$0.985438\pi$
$824$	0.870816	−	1.50830i	0.0303363	−	0.0525440i
$825$	33.8546	−	20.1163i	1.17867	−	0.700361i
$826$	1.99979	+	3.46374i	0.0695816	+	0.120519i
$827$	−0.131104	+	0.403496i	−0.00455892	+	0.0140309i	−0.953310	−	0.301993i	$-0.902348\pi$
$827$	−0.131104	+	0.403496i	−0.00455892	+	0.0140309i	0.948751	+	0.316024i	$0.102348\pi$
$828$	−0.222042	−	0.107067i	−0.00771648	−	0.00372083i
$829$	−15.0808	−	10.9568i	−0.523778	−	0.380547i	0.294247	−	0.955729i	$-0.404931\pi$
$829$	−15.0808	−	10.9568i	−0.523778	−	0.380547i	−0.818025	+	0.575182i	$0.804931\pi$
$830$	2.59512	−	67.4032i	0.0900780	−	2.33960i
$831$	37.8087	−	7.43728i	1.31157	−	0.257997i
$832$	−1.02898	+	1.78225i	−0.0356736	+	0.0617885i
$833$	1.13741	+	10.8217i	0.0394088	+	0.374950i
$834$	−38.7906	−	29.0947i	−1.34321	−	1.00747i
$835$	14.4098	−	4.07625i	0.498673	−	0.141064i
$836$	−7.41748	+	22.8286i	−0.256539	+	0.789545i
$837$	1.98419	+	33.5417i	0.0685835	+	1.15937i
$838$	6.49962	+	20.0038i	0.224526	+	0.691019i
$839$	28.4120	−	6.03916i	0.980892	−	0.208495i	0.310558	−	0.950554i	$-0.399484\pi$
$839$	28.4120	−	6.03916i	0.980892	−	0.208495i	0.670334	+	0.742059i	$0.266151\pi$
$840$	−2.86872	+	10.6494i	−0.0989803	+	0.367439i
$841$	24.2415	+	5.15270i	0.835915	+	0.177679i
$842$	−3.98670	−	37.9309i	−0.137391	−	1.30718i
$843$	15.9603	+	7.39888i	0.549702	+	0.254831i
$844$	−3.00805	−	1.33927i	−0.103541	−	0.0460996i
$845$	−6.88026	+	27.1808i	−0.236688	+	0.935047i
$846$	−4.38235	−	58.8750i	−0.150668	−	2.02416i
$847$	10.8694	+	7.89708i	0.373477	+	0.271347i
$848$	6.43322	−	1.36742i	0.220918	−	0.0469575i
$849$	−0.118102	−	1.31592i	−0.00405326	−	0.0451624i
$850$	6.80151	−	16.4937i	0.233290	−	0.565730i
$851$	−0.153613	+	0.266066i	−0.00526580	+	0.00912063i
$852$	−17.5426	−	4.00861i	−0.600998	−	0.137333i
$853$	−1.83844	+	17.4915i	−0.0629468	+	0.598899i	0.916896	+	0.399127i	$0.130687\pi$
$853$	−1.83844	+	17.4915i	−0.0629468	+	0.598899i	−0.979842	+	0.199772i	$0.935980\pi$
$854$	7.05296	+	5.12428i	0.241347	+	0.175349i
$855$	−32.1057	−	33.1860i	−1.09799	−	1.13494i
$856$	−31.6559	+	22.9993i	−1.08198	+	0.786101i
$857$	−4.22020	−	7.30960i	−0.144159	−	0.249691i	0.784900	−	0.619623i	$-0.212714\pi$
$857$	−4.22020	−	7.30960i	−0.144159	−	0.249691i	−0.929059	+	0.369932i	$0.879381\pi$
$858$	8.72788	−	1.71685i	0.297965	−	0.0586122i
$859$	33.0228	+	7.01920i	1.12672	+	0.239492i	0.733326	−	0.679877i	$-0.237967\pi$
$859$	33.0228	+	7.01920i	1.12672	+	0.239492i	0.393396	+	0.919369i	$0.371300\pi$
$860$	−0.928383	+	1.88632i	−0.0316576	+	0.0643229i
$861$	−3.84751	−	12.4845i	−0.131123	−	0.425469i
$862$	14.6004	−	16.2154i	0.497291	−	0.552298i
$863$	12.9265	+	39.7837i	0.440023	+	1.35425i	0.887851	+	0.460132i	$0.152198\pi$
$863$	12.9265	+	39.7837i	0.440023	+	1.35425i	−0.447828	+	0.894120i	$0.647802\pi$
$864$	−11.5506	+	18.0511i	−0.392960	+	0.614111i
$865$	9.54714	+	23.8755i	0.324613	+	0.811790i
$866$	−26.2641	+	29.1693i	−0.892492	+	0.991213i
$867$	−6.94591	+	20.3203i	−0.235896	+	0.690114i
$868$	−3.44234	+	5.96231i	−0.116841	+	0.202374i
$869$	4.26748	+	40.6024i	0.144764	+	1.37734i
$870$	12.7831	−	3.40696i	0.433388	−	0.115507i
$871$	1.00900	−	9.60000i	0.0341887	−	0.325283i
$872$	−21.7493	−	15.8018i	−0.736523	−	0.535115i
$873$	−4.39425	+	32.3177i	−0.148723	+	1.09379i
$874$	−1.22679			−0.0414967
$875$	−7.90474	+	13.3584i	−0.267229	+	0.451596i
$876$	0.703473	+	7.83826i	0.0237681	+	0.264830i
$877$	−19.1882	−	21.3106i	−0.647938	−	0.719608i	0.326266	−	0.945278i	$-0.394210\pi$
$877$	−19.1882	−	21.3106i	−0.647938	−	0.719608i	−0.974204	+	0.225670i	$0.927543\pi$
$878$	12.3175	−	5.48408i	0.415694	−	0.185079i
$879$	5.85692	−	9.79724i	0.197549	−	0.330453i
$880$	−47.1926	−	17.3681i	−1.59086	−	0.585477i
$881$	−11.7352	+	8.52611i	−0.395368	+	0.287252i	−0.767652	−	0.640867i	$-0.778575\pi$
$881$	−11.7352	+	8.52611i	−0.395368	+	0.287252i	0.372283	+	0.928119i	$0.378575\pi$
$882$	8.55078	−	23.8250i	0.287920	−	0.802229i
$883$	−42.8896	+	31.1611i	−1.44335	+	1.04865i	−0.456019	+	0.889970i	$0.650725\pi$
$883$	−42.8896	+	31.1611i	−1.44335	+	1.04865i	−0.987329	+	0.158684i	$0.949275\pi$
$884$	0.747387	−	0.830057i	0.0251373	−	0.0279178i
$885$	0.359986	−	6.69802i	0.0121008	−	0.225152i
$886$	−0.565995	−	0.628601i	−0.0190150	−	0.0211183i
$887$	8.79953	+	1.87040i	0.295459	+	0.0628018i	0.353256	−	0.935527i	$-0.385074\pi$
$887$	8.79953	+	1.87040i	0.295459	+	0.0628018i	−0.0577971	+	0.998328i	$0.518408\pi$
$888$	8.14932	+	6.11235i	0.273473	+	0.205117i
$889$	30.1308	−	6.40449i	1.01055	−	0.214800i
$890$	−28.0268	+	1.85914i	−0.939461	+	0.0623185i
$891$	−40.4741	+	6.05894i	−1.35593	+	0.202982i
$892$	−10.0558	+	7.30599i	−0.336694	+	0.244623i
$893$	−40.7174	−	70.5246i	−1.36256	−	2.36001i
$894$	−14.8726	+	43.5100i	−0.497415	+	1.45519i
$895$	−4.84931	+	9.85297i	−0.162094	+	0.329349i
$896$	16.8561	−	7.50483i	0.563123	−	0.250719i
$897$	0.0613354	+	0.110069i	0.00204793	+	0.00367510i
$898$	11.7571	−	2.49905i	0.392340	−	0.0833944i
$899$	−13.2788			−0.442872
$900$	−8.56910	+	7.67437i	−0.285637	+	0.255812i
$901$	2.85269			0.0950369
$902$	40.1946	−	8.54362i	1.33833	−	0.284471i
$903$	1.51275	−	2.53047i	0.0503411	−	0.0842089i
$904$	−13.0475	+	5.80914i	−0.433955	+	0.193209i
$905$	3.35176	+	3.26000i	0.111416	+	0.108366i
$906$	−15.9474	−	18.2625i	−0.529818	−	0.606733i
$907$	13.0147	+	22.5421i	0.432145	+	0.748498i	0.997058	−	0.0766530i	$-0.0244234\pi$
$907$	13.0147	+	22.5421i	0.432145	+	0.748498i	−0.564912	+	0.825151i	$0.691090\pi$
$908$	−5.71538	+	4.15247i	−0.189672	+	0.137804i
$909$	−17.3461	−	32.2732i	−0.575333	−	1.07044i
$910$	−2.69385	+	2.24404i	−0.0893003	+	0.0743893i
$911$	−3.92226	+	0.833703i	−0.129950	+	0.0276218i	−0.272428	−	0.962176i	$-0.587827\pi$
$911$	−3.92226	+	0.833703i	−0.129950	+	0.0276218i	0.142477	+	0.989798i	$0.454493\pi$
$912$	−7.05455	+	58.5396i	−0.233600	+	1.93844i
$913$	−80.6628	−	17.1454i	−2.66955	−	0.567430i
$914$	−17.6760	−	19.6312i	−0.584670	−	0.649342i
$915$	−5.22143	−	13.6567i	−0.172615	−	0.451477i
$916$	−4.21026	+	4.67597i	−0.139111	+	0.154498i
$917$	−13.0533	+	9.48377i	−0.431058	+	0.313182i
$918$	−13.0220	+	13.1983i	−0.429788	+	0.435610i
$919$	0.331871	−	0.241118i	0.0109474	−	0.00795375i	−0.582298	−	0.812975i	$-0.697846\pi$
$919$	0.331871	−	0.241118i	0.0109474	−	0.00795375i	0.593245	+	0.805022i	$0.297846\pi$
$920$	0.0189068	−	0.491067i	0.000623339	−	0.0161900i
$921$	34.9953	+	0.532353i	1.15314	+	0.0175416i
$922$	−50.1567	+	22.3312i	−1.65182	+	0.735439i
$923$	6.15481	+	6.83561i	0.202588	+	0.224997i
$924$	−7.60779	−	3.52682i	−0.250278	−	0.116024i
$925$	8.74557	+	11.3604i	0.287552	+	0.373526i
$926$	−30.6303			−1.00657
$927$	−2.35750	+	0.964814i	−0.0774306	+	0.0316887i
$928$	−6.85175	−	4.97808i	−0.224920	−	0.163414i
$929$	0.704207	−	6.70008i	0.0231043	−	0.219822i	−0.976878	−	0.213799i	$-0.931416\pi$
$929$	0.704207	−	6.70008i	0.0231043	−	0.219822i	0.999982	−	0.00602306i	$-0.00191721\pi$
$930$	37.1431	−	18.8630i	1.21797	−	0.618543i
$931$	−3.64970	−	34.7246i	−0.119614	−	1.13805i
$932$	−3.17656	+	5.50196i	−0.104052	+	0.180223i
$933$	20.3643	+	23.3206i	0.666698	+	0.763484i
$934$	−20.5261	+	22.7966i	−0.671635	+	0.745926i
$935$	−18.4558	−	11.6244i	−0.603570	−	0.380160i
$936$	3.86673	−	1.58247i	0.126388	−	0.0517246i
$937$	−13.0786	−	40.2519i	−0.427260	−	1.31497i	−0.900814	−	0.434206i	$-0.857029\pi$
$937$	−13.0786	−	40.2519i	−0.427260	−	1.31497i	0.473554	−	0.880765i	$-0.342971\pi$
$938$	−21.9688	+	24.3988i	−0.717305	+	0.796648i
$939$	21.6237	−	23.2931i	0.705662	−	0.760141i
$940$	−17.9468	+	9.46030i	−0.585359	+	0.308561i
$941$	−51.2834	−	10.9006i	−1.67179	−	0.355350i	−0.727919	−	0.685663i	$-0.759512\pi$
$941$	−51.2834	−	10.9006i	−1.67179	−	0.355350i	−0.943871	+	0.330314i	$0.892846\pi$
$942$	0.0793475	−	0.232131i	0.00258528	−	0.00756325i
$943$	0.291050	+	0.504114i	0.00947790	+	0.0164162i
$944$	−6.92961	+	5.03466i	−0.225540	+	0.163864i
$945$	12.8521	−	9.74836i	0.418077	−	0.317114i
$946$	7.50241	+	5.45082i	0.243924	+	0.177221i
$947$	−0.245164	+	2.33258i	−0.00796675	+	0.0757985i	−0.997783	−	0.0665533i	$-0.978800\pi$
$947$	−0.245164	+	2.33258i	−0.00796675	+	0.0757985i	0.989816	+	0.142352i	$0.0454664\pi$
$948$	−3.51227	−	11.3967i	−0.114073	−	0.370146i
$949$	2.01136	−	3.48378i	0.0652915	−	0.113088i
$950$	−21.8246	+	52.9249i	−0.708084	+	1.71711i
$951$	4.98595	+	2.31139i	0.161681	+	0.0749519i
$952$	5.97517	−	1.27006i	0.193656	−	0.0411629i
$953$	−7.72986	−	5.61607i	−0.250395	−	0.181922i	0.455507	−	0.890232i	$-0.349458\pi$
$953$	−7.72986	−	5.61607i	−0.250395	−	0.181922i	−0.705902	+	0.708310i	$0.749458\pi$
$954$	−5.97752	−	2.88232i	−0.193530	−	0.0933186i
$955$	−19.4306	−	12.2384i	−0.628759	−	0.396026i
$956$	0.756054	+	0.336617i	0.0244525	+	0.0108870i
$957$	−1.44574	−	16.1088i	−0.0467341	−	0.520723i
$958$	−4.01328	−	38.1839i	−0.129663	−	1.23366i
$959$	−22.4924	−	4.78090i	−0.726316	−	0.154383i
$960$	−11.5921	−	1.85186i	−0.374134	−	0.0597686i
$961$	−10.5779	+	2.24839i	−0.341221	+	0.0725288i
$962$	1.00071	+	3.07987i	0.0322642	+	0.0992989i
$963$	57.2028	+	1.74076i	1.84334	+	0.0560951i
$964$	−5.94735	+	18.3041i	−0.191551	+	0.589534i
$965$	−3.69043	−	1.35817i	−0.118799	−	0.0437211i
$966$	0.0512760	−	0.425495i	0.00164978	−	0.0136901i
$967$	−2.15909	−	20.5424i	−0.0694318	−	0.660599i	−0.972786	−	0.231705i	$-0.925570\pi$
$967$	−2.15909	−	20.5424i	−0.0694318	−	0.660599i	0.903354	−	0.428895i	$-0.141097\pi$
$968$	−9.92488	+	17.1904i	−0.318998	+	0.552520i
$969$	−8.27208	+	24.2000i	−0.265738	+	0.777417i
$970$	38.9100	−	11.0068i	1.24932	−	0.353408i
$971$	24.5224	+	17.8166i	0.786962	+	0.571761i	0.907060	−	0.421001i	$-0.138321\pi$
$971$	24.5224	+	17.8166i	0.786962	+	0.571761i	−0.120098	+	0.992762i	$0.538321\pi$
$972$	11.2589	−	4.01850i	0.361130	−	0.128894i
$973$	7.22044	−	22.2222i	0.231477	−	0.712412i
$974$	−9.49335	−	16.4430i	−0.304186	−	0.526866i
$975$	5.83965	−	0.687935i	0.187019	−	0.0220316i
$976$	−9.33514	+	16.1689i	−0.298810	+	0.517555i
$977$	−15.7527	−	17.4951i	−0.503973	−	0.559719i	0.436448	−	0.899729i	$-0.356236\pi$
$977$	−15.7527	−	17.4951i	−0.503973	−	0.559719i	−0.940422	+	0.340010i	$0.889570\pi$
$978$	17.3010	+	31.0474i	0.553224	+	0.992786i
$979$	−3.58946	+	34.1514i	−0.114719	+	1.09148i
$980$	−8.67937	+	0.575740i	−0.277252	+	0.0183913i
$981$	11.0073	+	37.7474i	0.351437	+	1.20518i
$982$	66.1926			2.11229
$983$	17.6593	+	7.86243i	0.563245	+	0.250773i	0.668550	−	0.743667i	$-0.266915\pi$
$983$	17.6593	+	7.86243i	0.563245	+	0.250773i	−0.105305	+	0.994440i	$0.533582\pi$
$984$	17.7497	−	7.58132i	0.565840	−	0.241684i
$985$	1.56459	−	3.17899i	0.0498521	−	0.101291i
$986$	−4.90295	−	5.44528i	−0.156142	−	0.173413i
$987$	26.1624	−	11.1746i	0.832758	−	0.355691i
$988$	−2.39821	+	2.66348i	−0.0762971	+	0.0847365i
$989$	−0.0405939	+	0.124935i	−0.00129081	+	0.00397271i
$990$	26.9271	+	43.0054i	0.855800	+	1.36680i
$991$	−0.458610	−	1.41146i	−0.0145682	−	0.0448364i	0.943508	−	0.331349i	$-0.107504\pi$
$991$	−0.458610	−	1.41146i	−0.0145682	−	0.0448364i	−0.958076	+	0.286513i	$0.907504\pi$
$992$	−24.3635	−	10.8473i	−0.773540	−	0.344402i
$993$	−23.1911	−	10.7509i	−0.735947	−	0.341171i
$994$	−3.27021	−	31.1140i	−0.103725	−	0.986876i
$995$	1.84036	+	10.6600i	0.0583433	+	0.337944i
$996$	24.0859	+	0.366397i	0.763189	+	0.0116097i
$997$	1.65392	−	15.7360i	0.0523803	−	0.498365i	−0.936609	−	0.350377i	$-0.886053\pi$
$997$	1.65392	−	15.7360i	0.0523803	−	0.498365i	0.988989	−	0.147988i	$-0.0472798\pi$
$998$	18.6267	−	57.3271i	0.589619	−	1.81466i
$999$	−3.95292	−	14.3653i	−0.125065	−	0.454496i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	225.2.q.a.121.22	yes	224
3.2	odd	2		675.2.r.a.496.7		224
9.2	odd	6		675.2.r.a.46.22		224
9.7	even	3	inner	225.2.q.a.196.7	yes	224
25.6	even	5	inner	225.2.q.a.31.7	✓	224
75.56	odd	10		675.2.r.a.631.22		224
225.56	odd	30		675.2.r.a.181.7		224
225.106	even	15	inner	225.2.q.a.106.22	yes	224

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
225.2.q.a.31.7	✓	224	25.6	even	5	inner
225.2.q.a.106.22	yes	224	225.106	even	15	inner
225.2.q.a.121.22	yes	224	1.1	even	1	trivial
225.2.q.a.196.7	yes	224	9.7	even	3	inner
675.2.r.a.46.22		224	9.2	odd	6
675.2.r.a.181.7		224	225.56	odd	30
675.2.r.a.496.7		224	3.2	odd	2
675.2.r.a.631.22		224	75.56	odd	10

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 225 = 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	225.q (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(1.62705 - 0.345839i) q^{2} +(1.73185 + 0.0263451i) q^{3} +(0.700584 - 0.311920i) q^{4} +(-0.380412 - 2.20347i) q^{5} +(2.82691 - 0.556077i) q^{6} +(0.694163 + 1.20233i) q^{7} +(-1.65942 + 1.20564i) q^{8} +(2.99861 + 0.0912516i) q^{9} +(-1.38100 - 3.45359i) q^{10} +(-4.44787 + 0.945423i) q^{11} +(1.22152 - 0.521742i) q^{12} +(-0.664131 - 0.141165i) q^{13} +(1.54525 + 1.71617i) q^{14} +(-0.600766 - 3.82611i) q^{15} +(-3.30929 + 3.67534i) q^{16} +(-1.73545 + 1.26088i) q^{17} +(4.91044 - 0.888568i) q^{18} +(5.56870 - 4.04590i) q^{19} +(-0.953818 - 1.42506i) q^{20} +(1.17051 + 2.10054i) q^{21} +(-6.90992 + 3.07649i) q^{22} +(-0.0716950 - 0.0796254i) q^{23} +(-2.90563 + 2.04427i) q^{24} +(-4.71057 + 1.67645i) q^{25} -1.12939 q^{26} +(5.19074 + 0.237033i) q^{27} +(0.861350 + 0.625807i) q^{28} +(-0.214650 + 2.04226i) q^{29} +(-2.30069 - 6.01748i) q^{30} +(0.675922 + 6.43096i) q^{31} +(-2.06213 + 3.57172i) q^{32} +(-7.72795 + 1.52015i) q^{33} +(-2.38760 + 2.65170i) q^{34} +(2.38522 - 1.98695i) q^{35} +(2.12924 - 0.871398i) q^{36} +(-0.886060 - 2.72701i) q^{37} +(7.66130 - 8.50874i) q^{38} +(-1.14646 - 0.261974i) q^{39} +(3.28786 + 3.19785i) q^{40} +(-5.31403 - 1.12953i) q^{41} +(2.63092 + 3.01286i) q^{42} +(-0.613014 - 1.06177i) q^{43} +(-2.82121 + 2.04973i) q^{44} +(-0.939638 - 6.64207i) q^{45} +(-0.144189 - 0.104759i) q^{46} +(1.23665 - 11.7660i) q^{47} +(-5.82802 + 6.27796i) q^{48} +(2.53627 - 4.39296i) q^{49} +(-7.08454 + 4.35677i) q^{50} +(-3.03876 + 2.13793i) q^{51} +(-0.509312 + 0.108258i) q^{52} +(-1.07586 - 0.781661i) q^{53} +(8.52756 - 1.40950i) q^{54} +(3.77524 + 9.44110i) q^{55} +(-2.60148 - 1.15825i) q^{56} +(9.75074 - 6.86018i) q^{57} +(0.357048 + 3.39709i) q^{58} +(1.69407 + 0.360086i) q^{59} +(-1.61433 - 2.49312i) q^{60} +(3.69259 - 0.784884i) q^{61} +(3.32384 + 10.2297i) q^{62} +(1.97181 + 3.66865i) q^{63} +(0.936638 - 2.88268i) q^{64} +(-0.0584104 + 1.51709i) q^{65} +(-12.0480 + 5.14599i) q^{66} +(1.48608 + 14.1391i) q^{67} +(-0.822536 + 1.42467i) q^{68} +(-0.122067 - 0.139788i) q^{69} +(3.19370 - 4.05776i) q^{70} +(-10.9600 - 7.96294i) q^{71} +(-5.08598 + 3.46382i) q^{72} +(-1.83085 + 5.63478i) q^{73} +(-2.38477 - 4.13054i) q^{74} +(-8.20217 + 2.77927i) q^{75} +(2.63935 - 4.57148i) q^{76} +(-4.22425 - 4.69151i) q^{77} +(-1.95594 - 0.0297540i) q^{78} +(0.938478 - 8.92902i) q^{79} +(9.35740 + 5.89378i) q^{80} +(8.98335 + 0.547256i) q^{81} -9.03682 q^{82} +(16.5673 + 7.37623i) q^{83} +(1.47524 + 1.10650i) q^{84} +(3.43850 + 3.34436i) q^{85} +(-1.36460 - 1.51555i) q^{86} +(-0.425545 + 3.53123i) q^{87} +(6.24105 - 6.93138i) q^{88} +(2.33361 - 7.18212i) q^{89} +(-3.82592 - 10.4820i) q^{90} +(-0.291288 - 0.896494i) q^{91} +(-0.0750652 - 0.0334212i) q^{92} +(1.00117 + 11.1553i) q^{93} +(-2.05704 - 19.5715i) q^{94} +(-11.0334 - 10.7314i) q^{95} +(-3.66541 + 6.13136i) q^{96} +(-1.13640 + 10.8121i) q^{97} +(2.60738 - 8.02469i) q^{98} +(-13.4237 + 2.42908i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 224 q - 3 q^{2} - 8 q^{3} + 23 q^{4} - 8 q^{5} - 10 q^{6} - 8 q^{7} - 20 q^{8} - 8 q^{9} - 20 q^{10} - 11 q^{11} - 4 q^{12} - 3 q^{13} + q^{14} - 48 q^{15} + 23 q^{16} - 24 q^{17} - 12 q^{19} + q^{20}+ \cdots - 20 q^{99}+O(q^{100}) \) 224 * q - 3 * q^2 - 8 * q^3 + 23 * q^4 - 8 * q^5 - 10 * q^6 - 8 * q^7 - 20 * q^8 - 8 * q^9 - 20 * q^10 - 11 * q^11 - 4 * q^12 - 3 * q^13 + q^14 - 48 * q^15 + 23 * q^16 - 24 * q^17 - 12 * q^19 + q^20 + 15 * q^21 - 11 * q^22 + q^23 - 30 * q^24 - 16 * q^25 - 136 * q^26 + 7 * q^27 + 4 * q^28 - 15 * q^29 - 24 * q^30 + 3 * q^31 + 12 * q^32 - 5 * q^33 + q^34 + 14 * q^35 + 38 * q^36 - 24 * q^37 + 55 * q^38 + 20 * q^39 + q^40 - 19 * q^41 - 38 * q^42 - 8 * q^43 + 4 * q^44 - 38 * q^45 - 20 * q^46 - 10 * q^47 - 25 * q^48 - 72 * q^49 - 3 * q^50 - 26 * q^51 - 25 * q^52 - 12 * q^53 + 53 * q^54 - 20 * q^55 - 60 * q^56 + 38 * q^57 - 23 * q^58 - 30 * q^59 - 33 * q^60 - 3 * q^61 - 44 * q^62 + 46 * q^63 - 44 * q^64 + 51 * q^65 - 134 * q^66 - 12 * q^67 - 156 * q^68 + 4 * q^69 - 16 * q^70 + 42 * q^71 + 74 * q^72 - 12 * q^73 + 90 * q^74 + 67 * q^75 - 8 * q^76 + 31 * q^77 - 92 * q^78 - 15 * q^79 + 298 * q^80 - 104 * q^81 + 8 * q^82 + 59 * q^83 + 115 * q^84 - 11 * q^85 + 9 * q^86 - 59 * q^87 - 23 * q^88 + 106 * q^89 + 107 * q^90 + 30 * q^91 + 11 * q^92 + 32 * q^93 + 25 * q^94 + 7 * q^95 + 35 * q^96 - 21 * q^97 + 146 * q^98 - 20 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more